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Words: 19k
Articles: 786
Table of contents
19k
786
Field
Algebra
61
2
Algebraically closed field
Field
24
Characteristic of a field
Field
22
Polynomial
Algebra
256
13
Monic polynomial
Polynomial
7
Root of a polynomial
Polynomial
51
2
Multiple root
Root of a polynomial
23
Common root
Root of a polynomial
15
Elementary symmetric polynomial
Polynomial
62
2
Fundamental theorem of symmetric polynomials
Elementary symmetric polynomial
19
Newton identities
Elementary symmetric polynomial
24
Irreducible polynomial
Polynomial
33
Polynomial division
Polynomial
22
Degree of a polynomial
Polynomial
45
1
Lagrange root bound over a field
Degree of a polynomial
29
Quadratic function
Polynomial
23
1
Quadratic equation
Quadratic function
10
Algebraic number theory
Algebra
2k
55
Algebraic integer
Algebraic number theory
24
Ring of integers of a quadratic field
Algebraic number theory
130
3
Splitting of rational primes in a quadratic field
Ring of integers of a quadratic field
105
2
Ramification of a prime
Splitting of rational primes in a quadratic field
20
Splitting of three in Q of square root minus p
Splitting of rational primes in a quadratic field
32
Discriminant of a biquadratic field
Algebraic number theory
18
Algebraic integer module criterion
Algebraic number theory
63
2
Ring generated by algebraic integers
Algebraic integer module criterion
18
Integral dependence is transitive
Algebraic integer module criterion
21
Integral basis
Algebraic number theory
85
2
Field discriminant
Integral basis
68
1
Discriminant-index formula for an integral lattice
Field discriminant
51
Cubic field of discriminant minus 307
Algebraic number theory
95
2
Integral basis of the cubic field of discriminant minus 307
Cubic field of discriminant minus 307
42
Prime ideals above two and three in the cubic field of discriminant minus 307
Cubic field of discriminant minus 307
24
Field norm
Algebraic number theory
68
2
Norm obstruction to being a square
Field norm
24
Unit from norm one or minus one
Field norm
21
Minkowski convex body theorem
Algebraic number theory
63
1
Minkowski embedding of a real quadratic field
Minkowski convex body theorem
35
Mahler measure
Algebraic number theory
94
1
Mahler-measure norm argument at measure two
Mahler measure
86
Dirichlet unit theorem
Algebraic number theory
321
9
Units of the quadratic field Q square root of five
Dirichlet unit theorem
18
Finite relative unit quotient over a real quadratic field
Dirichlet unit theorem
69
Logarithmic embedding of number field units
Dirichlet unit theorem
148
3
Kernel of the logarithmic unit embedding
Logarithmic embedding of number field units
47
Dirichlet unit lattice
Logarithmic embedding of number field units
68
1
Archimedean balancing of a principal ideal generator
Dirichlet unit lattice
40
Units of Q of square root ten
Dirichlet unit theorem
16
Units of Q of square root minus three
Dirichlet unit theorem
11
Unit group of the fifth cyclotomic field
Dirichlet unit theorem
27
Field trace
Algebraic number theory
78
3
Trace form of a number field
Field trace
34
1
Nondegeneracy of the trace form of a number field
Trace form of a number field
19
Trace and norm integrality criterion for a quadratic extension
Field trace
22
Fractional ideal
Algebraic number theory
41
1
Integral ideal
Fractional ideal
16
Ideal norm
Algebraic number theory
22
Ideal class group
Algebraic number theory
270
8
Minkowski bound for ideal classes
Ideal class group
109
2
Class group of Q of cube root of three
Minkowski bound for ideal classes
39
Ideal class group of Q of square root of minus thirty-three
Minkowski bound for ideal classes
44
Order of an ideal class
Ideal class group
79
1
Odd-order obstruction for a split prime in an imaginary quadratic field
Order of an ideal class
58
Bounded-norm ideal representatives
Ideal class group
27
Finiteness of the ideal class group
Ideal class group
18
Ideal classes are torsion
Ideal class group
22
Unique factorization of ideals in a number field
Algebraic number theory
54
1
Dedekind factorization theorem
Unique factorization of ideals in a number field
32
Dedekind zeta function
Algebraic number theory
86
2
Euler product for the Dedekind zeta function
Dedekind zeta function
27
Quadratic Dedekind zeta factorization
Dedekind zeta function
43
Primary ideal
Algebraic number theory
53
1
Radical of a primary ideal
Primary ideal
33
Galois theory
Algebra
2k
76
Frobenius endomorphism
Galois theory
33
Formal derivative in positive characteristic
Galois theory
53
1
Polynomial with zero formal derivative in characteristic p
Formal derivative in positive characteristic
29
Separable polynomial
Galois theory
26
Automorphism-count divisibility theorem
Galois theory
31
Coprime-degree descent for powers
Galois theory
37
Algebraic element
Galois theory
57
1
Minimal polynomial of an algebraic element
Algebraic element
35
Primitive element of a field extension
Galois theory
17
Primitive element theorem
Galois theory
16
Finite separable simple extension implications
Galois theory
46
Biquadratic extension
Galois theory
42
Transitive subgroups of the symmetric group on four points
Galois theory
20
Dihedral Galois action on four radical roots
Galois theory
32
Field embedding
Galois theory
122
3
Linear independence of distinct field embeddings
Field embedding
67
1
Lagrange resolvent eigenvector for a cyclic field automorphism
Linear independence of distinct field embeddings
38
Extension count for field embeddings
Field embedding
34
Tower law for field extensions
Galois theory
12
Splitting field
Galois theory
250
4
Existence and uniqueness of splitting fields
Splitting field
65
Splitting field of x cubed minus two
Splitting field
30
Finite normal extension as a splitting field
Splitting field
61
Splitting field of a polynomial obtained by Frobenius substitution
Splitting field
69
Normal field extension
Galois theory
36
Separable field extension
Galois theory
51
1
Separable algebraic element
Separable field extension
36
Purely inseparable field extension
Galois theory
144
3
Purely inseparable algebraic element
Purely inseparable field extension
72
1
Minimal polynomial of a purely inseparable element
Purely inseparable algebraic element
56
Unique embedding extension through a purely inseparable extension
Purely inseparable field extension
50
Finite Galois extension
Galois theory
42
1
Normal and separable implies Galois
Finite Galois extension
28
Roots of unity in a finite field
Galois theory
32
Kummer extension of rational function fields
Galois theory
33
Galois group of a polynomial
Galois theory
75
1
Transitivity lifted through unique pth roots
Galois group of a polynomial
53
Irreducible factors after Frobenius substitution
Galois theory
119
1
Reducibility criterion after Frobenius substitution
Irreducible factors after Frobenius substitution
69
Frobenius cycle type
Galois theory
25
Dedekind factorization cycle test
Galois theory
27
Cyclotomic polynomial
Galois theory
385
12
Cyclotomic factorization
Cyclotomic polynomial
24
Separability of a cyclotomic polynomial modulo p
Cyclotomic polynomial
33
Galois embedding for a cyclotomic polynomial
Cyclotomic polynomial
38
Cyclotomic field
Cyclotomic polynomial
263
8
Roots of unity in a rational cyclotomic field
Cyclotomic field
20
Seventh cyclotomic field
Cyclotomic field
80
2
Quadratic Gaussian period in the seventh cyclotomic field
Seventh cyclotomic field
22
Real cubic subfield of the seventh cyclotomic field
Seventh cyclotomic field
24
Maximal cyclotomic extension
Cyclotomic field
113
3
Maximal cyclotomic extension of the real numbers
Maximal cyclotomic extension
22
Maximal cyclotomic extension of the rational numbers
Maximal cyclotomic extension
33
Maximal cyclotomic extension of a finite field
Maximal cyclotomic extension
33
Constructible field extension
Galois theory
77
1
Constructibility of the real seventeenth cyclotomic field
Constructible field extension
38
Fixed field
Galois theory
32
Artin fixed-field theorem
Galois theory
28
Galois correspondence
Galois theory
253
5
Normal subextension criterion
Galois correspondence
27
Subextensions of an abelian Galois extension
Galois correspondence
133
2
Cyclic Galois extension of the rational numbers of every finite degree
Subextensions of an abelian Galois extension
39
Finite extensions of the fixed field of a finite-order automorphism of an algebraically closed field
Subextensions of an abelian Galois extension
69
Subfields of the splitting field of x to the fourth minus seven
Galois correspondence
73
Polynomial discriminant
Galois theory
95
3
Vandermonde determinant
Polynomial discriminant
20
Discriminant of a depressed cubic
Polynomial discriminant
8
Discriminant criterion for an alternating Galois group
Polynomial discriminant
48
Lagrange resolvent for a cubic
Galois theory
54
2
Cubic resolvent
Lagrange resolvent for a cubic
30
1
Cardano formula
Cubic resolvent
19
Solvability by radicals
Galois theory
24
Galois group of an irreducible cubic
Galois theory
77
2
Splitting field of x cubed minus x minus one
Galois group of an irreducible cubic
37
Cubic discriminant criterion
Galois group of an irreducible cubic
16
Characteristic-two cubic resolvent
Galois theory
54
Representation theory
Algebra
2k
80
Group representation
Representation theory
41
1
Semisimple representation
Group representation
20
Maschke's theorem
Representation theory
42
Complex representation
Representation theory
314
10
Continuous representation of a topological group
Complex representation
22
Degree of a representation
Complex representation
11
Isomorphic representations
Complex representation
22
Faithful representation
Complex representation
218
5
Regular representation
Faithful representation
69
1
Faithful irreducible representation of a finite simple group
Regular representation
53
Spectrum orbit bound for a faithful symmetric-group representation
Faithful representation
54
Finite-dimensional representation obstruction from elementary abelian subgroups
Faithful representation
44
Real Heisenberg quotient has no faithful finite-dimensional representation
Faithful representation
42
One-dimensional representation kills the commutator subgroup
Complex representation
23
Representation of SU2
Representation theory
217
9
Homogeneous polynomial representation of SU2
Representation of SU2
37
1
Character of the homogeneous polynomial representation of SU2
Homogeneous polynomial representation of SU2
9
Classification of finite-dimensional representations of SU2
Representation of SU2
17
Self-duality of finite-dimensional SU2 representations
Representation of SU2
32
Central parity on SU2 tensor products
Representation of SU2
37
Clebsch-Gordan decomposition for SU2
Representation of SU2
78
3
Flip parity in the SU2 tensor square
Clebsch-Gordan decomposition for SU2
58
2
Exterior square of an SU2 irreducible representation
Flip parity in the SU2 tensor square
31
1
Second and third exterior powers of V4 of SU2
Exterior square of an SU2 irreducible representation
25
Character of an exterior square
Representation theory
7
Character of an exterior cube
Representation theory
11
Averaging over a finite group
Representation theory
21
Unitary representation
Representation theory
116
4
Unitarization of a finite-group representation
Unitary representation
26
Unitarization of a compact-group representation
Unitary representation
21
Representation of the circle group
Unitary representation
54
1
Central circle weight-space decomposition
Representation of the circle group
28
Character orthogonality
Representation theory
10
Character table
Representation theory
77
3
Irreducible character degree
Character table
41
2
Linear character
Irreducible character degree
15
Nonlinear irreducible character
Irreducible character degree
9
Character of a representation
Representation theory
19
Burnside lemma
Representation theory
72
1
Permutation representation of a two-transitive action
Burnside lemma
37
Permutation representation
Representation theory
131
3
Symmetric-group subset permutation representation
Permutation representation
75
1
Inclusion map between subset permutation modules
Symmetric-group subset permutation representation
40
Standard representation of the symmetric group
Permutation representation
30
Intertwining operator
Representation theory
21
Schur lemma
Representation theory
108
2
Proof of Schur lemma
Schur lemma
46
Cyclic-center obstruction to a faithful irreducible representation
Schur lemma
43
Dual representation
Representation theory
161
4
Character of a Hom representation
Dual representation
81
1
Two-sided regular representation decomposition
Character of a Hom representation
57
Invariant bilinear form as an intertwiner
Dual representation
66
1
Symmetric-or-alternating dichotomy for invariant forms
Invariant bilinear form as an intertwiner
30
Induced representation
Representation theory
422
12
Character formula for an induced representation
Induced representation
13
Induction from an abelian normal subgroup with a free character orbit
Induced representation
105
1
Irreducible characters of the affine semidirect product of orders eleven and five
Induction from an abelian normal subgroup with a free character orbit
50
Tensor identity for induced representations
Induced representation
29
Frobenius reciprocity
Induced representation
28
Mackey restriction formula
Induced representation
140
4
Mackey irreducibility criterion
Mackey restriction formula
40
Bruhat decomposition of SL2 over a finite field
Mackey restriction formula
79
2
Mackey inner product for the finite SL2 principal series
Bruhat decomposition of SL2 over a finite field
53
1
Irreducible principal series of finite SL2
Mackey inner product for the finite SL2 principal series
34
Square orbits of additive characters of a finite field
Induced representation
91
1
Induction from the diagonal subgroup of upper-triangular SL2
Square orbits of additive characters of a finite field
53
Irreducible representation
Representation theory
125
4
Eigenvalue orbit under conjugation
Irreducible representation
19
Irreducible complex representations of a finite dihedral group
Irreducible representation
97
2
Two-dimensional representations of a finite dihedral group
Irreducible complex representations of a finite dihedral group
57
1
Faithful irreducible representation of D8
Two-dimensional representations of a finite dihedral group
19
Infinite dihedral group
Representation theory
46
2
Representation of the infinite dihedral group
Infinite dihedral group
36
1
Induced two-dimensional dihedral representation
Representation of the infinite dihedral group
15
One-dimensional character
Representation theory
41
1
One-dimensional characters factor through the abelianization
One-dimensional character
24
Finite quotient representation
Representation theory
18
Indecomposable representation
Representation theory
43
2
Nonsplit extension of representations
Indecomposable representation
12
Unipotent representation
Indecomposable representation
16
Coding theory
Algebra
2k
63
Binary block code
Coding theory
49
1
Hamming distance
Binary block code
16
One-time pad
Coding theory
99
2
Perfect secrecy
One-time pad
23
Malleability of an additive one-time pad
One-time pad
33
Discrete memoryless channel
Coding theory
33
Shannon second coding theorem
Coding theory
27
Linear-feedback shift register
Coding theory
307
8
Feedback shift register
Linear-feedback shift register
32
Berlekamp-Massey algorithm
Linear-feedback shift register
51
1
Minimal recurrence for the binary prefix 11001011
Berlekamp-Massey algorithm
19
Period bound for a linear-feedback shift register
Linear-feedback shift register
24
Feedback-polynomial parity condition for maximal period
Linear-feedback shift register
39
Zero-run lower bound for a linear-feedback shift register
Linear-feedback shift register
62
1
Minimal linear-feedback shift register for the prefix 100000001
Zero-run lower bound for a linear-feedback shift register
28
Trace-generated maximal-period linear-feedback sequence
Linear-feedback shift register
65
Linear code
Coding theory
496
20
Even-weight binary code
Linear code
19
Binary repetition code
Linear code
11
Zero code
Linear code
12
Whole-space linear code
Linear code
12
Hamming weight
Linear code
14
Minimum Hamming distance of a linear code
Linear code
14
Generator matrix
Linear code
21
Parity-check matrix
Linear code
10
Parity-check extension of a linear code
Linear code
26
Punctured code
Linear code
34
Shortened code
Linear code
39
Dual code
Linear code
27
Reed-Muller code
Linear code
105
3
Bar product of binary linear codes
Reed-Muller code
36
1
Reed-Muller bar-product recursion
Bar product of binary linear codes
9
Dual of a Reed-Muller code
Reed-Muller code
31
Hamming code
Linear code
85
2
Binary simplex code
Hamming code
20
Perfectness of a Hamming code
Hamming code
41
Minimum-distance error-detection and correction guarantee
Linear code
40
Cyclic code
Coding theory
193
6
Generator polynomial of a cyclic code
Cyclic code
22
Dual of a cyclic code
Cyclic code
22
Binary cyclic codes of length seven
Cyclic code
28
BCH code
Cyclic code
96
2
Error locator polynomial
BCH code
26
BCH bound
BCH code
44
Parity extension
Coding theory
24
Hamming bound
Coding theory
22
Rabin cryptosystem
Coding theory
24
Discrete logarithm problem
Coding theory
24
Diffie-Hellman key exchange
Coding theory
38
Decipherable code
Coding theory
179
6
Prefix code
Decipherable code
158
5
Kraft inequality
Prefix code
52
1
Total length lower bound for a decipherable binary code
Kraft inequality
29
Shannon-Fano coding
Prefix code
14
Cumulative Shannon code
Prefix code
53
Entropy lower bound for prefix codes
Prefix code
21
Binary symmetric channel
Coding theory
115
3
Undetected error
Binary symmetric channel
32
Completely noisy binary symmetric channel
Binary symmetric channel
26
Positive-rate coding bound below one-quarter crossover
Binary symmetric channel
41
Maximum a posteriori decoding
Coding theory
18
Maximum-likelihood decoding
Coding theory
14
Minimum-distance decoding
Coding theory
25
Linear algebra
Algebra
5k
228
Cartesian basis
Linear algebra
13
Bilinear form
Linear algebra
174
5
Radical of a bilinear form
Bilinear form
23
Nondegenerate bilinear form
Bilinear form
96
2
Symplectic vector space
Nondegenerate bilinear form
39
Representation of a bilinear form relative to a nondegenerate bilinear form
Nondegenerate bilinear form
32
Inertia of a bilinear form
Bilinear form
30
Sesquilinear form
Linear algebra
67
2
Hermitian form
Sesquilinear form
44
1
Matrix of a Hermitian form
Hermitian form
32
Vector space
Linear algebra
685
36
Linear combination
Vector space
15
Scalar multiple
Vector space
19
Dimension of a vector space
Vector space
14
Direct sum
Vector space
88
2
Dimension formula for a sum of subspaces
Direct sum
13
Direct-sum complement
Direct sum
30
Linear independence
Vector space
25
1
Linear dependence
Linear independence
15
Basis
Vector space
12
Vector
Vector space
31
1
Cross product
Vector
23
Scalar
Vector space
13
Linear map
Vector space
450
23
First isomorphism theorem for vector spaces
Linear map
20
Linear isomorphism
Linear map
12
Linear function
Linear map
13
Linearity
Linear map
6
Superposition principle
Linear map
13
Linear operator
Linear map
83
3
Unitary operator
Linear operator
18
Conjugate linear operators
Linear operator
56
1
Conjugation operator on an endomorphism space
Conjugate linear operators
26
Matrix
Linear map
294
13
Matrix power
Matrix
23
Matrix element
Matrix
17
Matrix unit
Matrix
34
Matrix rank
Matrix
19
Identity matrix
Matrix
20
Rank-one matrix
Matrix
18
Upper bidiagonal matrix
Matrix
16
Matrix multiplication
Matrix
33
1
Outer product
Matrix multiplication
21
Upper Hessenberg matrix
Matrix
15
Permutation matrix
Matrix
27
Matrix representation of a linear map
Matrix
27
Kronecker product
Matrix
31
Singular value decomposition
Linear algebra
44
1
Singular value
Singular value decomposition
16
Unimodular matrix
Linear algebra
29
Householder reflection
Linear algebra
19
Change of basis
Linear algebra
Circulant matrix
Linear algebra
Invertible matrix
Linear algebra
Kernel of a linear map
Linear algebra
46
1
Rank-nullity theorem
Kernel of a linear map
46
Dual space
Linear algebra
254
9
Linear functional
Dual space
15
Dual basis
Dual space
16
Annihilator of a vector subspace
Dual space
14
Dual map
Dual space
130
3
Equality of row rank and column rank
Dual map
91
1
Simultaneous basis exchange from a nonzero minor
Equality of row rank and column rank
47
Duals of a subspace and its quotient
Dual map
21
Surjectivity of independent linear functionals
Dual space
31
Polynomial moment functional
Dual space
26
Rank of a matrix with affine columns
Linear algebra
42
Matrix determinant lemma
Linear algebra
Matrix inverse
Linear algebra
6
Similar matrix
Linear algebra
84
3
Similarity transformation
Similar matrix
31
Transpose similarity
Similar matrix
11
Real similarity from complex similarity
Similar matrix
42
Matrix trace
Linear algebra
24
Linear operator theory
Linear algebra
2k
76
Spectrum
Linear operator theory
24
Compression of a linear operator
Linear operator theory
46
Self-adjoint operator
Linear operator theory
123
6
Finite-dimensional spectral theorem
Self-adjoint operator
29
1
Orthonormal eigenbasis
Finite-dimensional spectral theorem
10
Laguerre differential operator on polynomials
Self-adjoint operator
76
3
Laguerre polynomial
Laguerre differential operator on polynomials
39
2
Generalized Laguerre polynomial
Laguerre polynomial
39
1
Rodrigues formula
Generalized Laguerre polynomial
22
Real spectral theorem
Linear operator theory
18
Power method
Linear operator theory
252
7
Quadratic Rayleigh-quotient improvement for the power method
Power method
40
Active spectrum of the power method
Power method
40
Inverse iteration
Power method
81
1
Convergence of fixed-shift inverse iteration
Inverse iteration
53
Subspace iteration
Power method
67
2
Dominant invariant subspace
Subspace iteration
16
Power method with a dominant eigenvalue cluster
Subspace iteration
23
Characteristic polynomial
Linear operator theory
70
2
Real parameter avoiding a singular matrix pencil
Characteristic polynomial
26
Triangularization over an algebraically closed field
Characteristic polynomial
30
Eigenvalue interlacing
Linear operator theory
18
Jordan normal form
Linear operator theory
271
8
Algebraic multiplicity
Jordan normal form
32
Geometric multiplicity
Jordan normal form
24
Jordan block
Jordan normal form
48
1
Nilpotent Jordan block
Jordan block
34
Jordan normal form of conjugation on two-by-two matrices
Jordan normal form
27
Characteristic and minimal polynomials determine similarity in dimension three
Jordan normal form
85
Generalized eigenvector
Jordan normal form
55
1
Generalized eigenspaces for distinct eigenvalues form a direct sum
Generalized eigenvector
39
Matrix exponential
Linear operator theory
47
1
Laplace transform of a matrix exponential
Matrix exponential
22
Minimal polynomial
Linear operator theory
77
2
Kernel decomposition for coprime polynomials
Minimal polynomial
19
Minimal polynomial bound from a triangular invariant flag
Minimal polynomial
35
Jacobson lemma for a commuting commutator
Linear operator theory
60
Translation finite-difference operator
Linear operator theory
84
1
Mixed finite difference of a polynomial
Translation finite-difference operator
36
Nilpotent linear map
Linear operator theory
11
Eigenvalue
Linear operator theory
337
16
Eigenfunction
Eigenvalue
19
Eigenvector
Eigenvalue
37
2
Right eigenvector
Eigenvector
7
Left eigenvector
Eigenvector
14
Eigenspace
Eigenvalue
17
1
Eigenbasis
Eigenspace
9
Simple eigenvalue
Eigenvalue
56
2
Eigenvalue sensitivity
Simple eigenvalue
48
1
First-order perturbation of a simple eigenvalue
Eigenvalue sensitivity
17
Diagonalizable matrix
Eigenvalue
192
6
Diagonalizability inherited from an invertible power
Diagonalizable matrix
44
Complex similarity of real matrices implies real similarity
Diagonalizable matrix
48
Distinct eigenvalues imply diagonalizability
Diagonalizable matrix
19
Spectral decomposition
Diagonalizable matrix
68
2
Dominant eigenvalue
Spectral decomposition
25
Spectral gap
Spectral decomposition
31
Adjoint matrix
Linear operator theory
12
Unitary matrix
Linear operator theory
22
Normal matrix
Linear operator theory
28
1
Unitary diagonalization of a normal matrix
Normal matrix
20
Schur triangularization
Linear operator theory
33
Unilateral shift operator
Linear operator theory
69
2
Point spectrum
Unilateral shift operator
11
Wandering-vector characterization of a unilateral shift
Unilateral shift operator
37
Rayleigh quotient
Linear operator theory
251
6
Rayleigh quotient iteration
Rayleigh quotient
28
Rayleigh-Ritz variational principle
Rayleigh quotient
203
4
Odd-state variational principle for an even potential
Rayleigh-Ritz variational principle
34
Gaussian variational bound for an attractive Gaussian well
Rayleigh-Ritz variational principle
40
Finite-subspace variational method
Rayleigh-Ritz variational principle
79
1
Two-mode variational bound for a linearly tilted square well
Finite-subspace variational method
37
Cyclic vector
Linear operator theory
14
Companion matrix
Linear operator theory
15
Invariant direct-sum decomposition
Linear operator theory
14
Rational canonical form
Linear operator theory
22
Multilinear algebra
Linear algebra
315
14
Tensor
Multilinear algebra
173
5
Covariant tensor
Tensor
17
Antisymmetric second-rank tensor
Tensor
20
Totally antisymmetric tensor
Tensor
36
Isotropic tensor
Tensor
41
Einstein notation
Tensor
18
Tensor contraction
Multilinear algebra
Reciprocal basis
Multilinear algebra
25
Scalar triple product
Multilinear algebra
32
1
Oriented volume
Scalar triple product
15
Determinant
Multilinear algebra
70
3
Multilinearity of the determinant
Determinant
18
Leibniz formula for determinants
Determinant
10
Tridiagonal determinant recurrence
Determinant
23
Linear system
Linear algebra
62
2
Linear equation
Linear system
20
Fredholm alternative for a matrix
Linear system
17
Symmetric and antisymmetric parts of a matrix
Linear algebra
15
Symmetric matrix
Linear algebra
16
Axis-angle decomposition
Linear algebra
36
1
Inverse of an axis-angle linear map
Axis-angle decomposition
14
Reflection matrix
Linear algebra
76
2
Reflection in a hyperplane
Reflection matrix
31
Composition of two plane reflections
Reflection matrix
26
Rotation matrix
Linear algebra
22
1
Rotational symmetry
Rotation matrix
11
Cartesian coordinate system
Linear algebra
34
1
Positive quadrant
Cartesian coordinate system
18
Matrix geometric series
Linear algebra
6
Adjugate matrix
Linear algebra
14
Matrix equivalence
Linear algebra
15
Rank inequality for a composition
Linear algebra
14
Schur complement
Linear algebra
17
Orthogonal similarity
Linear algebra
11
Product of symmetric matrices
Linear algebra
13
Inner product
Linear algebra
273
11
Orthonormal basis
Inner product
15
Gram matrix
Inner product
43
Pythagorean theorem in an inner-product space
Inner product
11
Orthogonal projection onto a finite-dimensional subspace
Inner product
88
2
Orthogonal projection matrix
Orthogonal projection onto a finite-dimensional subspace
18
Least-squares polynomial in an orthogonal-polynomial basis
Orthogonal projection onto a finite-dimensional subspace
38
Orthogonal vectors
Inner product
7
Nonorthogonal vectors
Inner product
20
Gram-Schmidt process
Inner product
89
2
QR decomposition
Gram-Schmidt process
24
Gram-Schmidt orthogonalization for a symmetric bilinear form
Gram-Schmidt process
39
Quadratic form
Linear algebra
398
17
Rank of a quadratic form
Quadratic form
15
Signature of a quadratic form
Quadratic form
24
Polarization identity
Quadratic form
66
1
Polarization argument for a vanishing quadratic form
Polarization identity
48
Positive semidefinite bilinear form
Quadratic form
24
Positive semidefinite matrix
Quadratic form
77
2
Principal square root of a positive semidefinite matrix
Positive semidefinite matrix
52
1
Polar decomposition of an invertible real matrix
Principal square root of a positive semidefinite matrix
23
Positive-definite matrix
Quadratic form
97
4
Sylvester's criterion
Positive-definite matrix
15
Spectral condition number of a positive-definite matrix
Positive-definite matrix
22
Hermitian positive-definite matrix
Positive-definite matrix
35
1
Toeplitz matrix
Hermitian positive-definite matrix
16
Sylvester's law of inertia
Quadratic form
24
Totally isotropic subspace
Quadratic form
29
Isotropic vector
Quadratic form
13
Quadratic form gradient
Quadratic form
12
Schur product theorem
Linear algebra
29
Orthogonal group
Linear algebra
110
4
Orthogonal matrix
Orthogonal group
17
Special orthogonal group
Orthogonal group
37
Skew-symmetric matrix
Orthogonal group
36
1
Cross-product matrix
Skew-symmetric matrix
29
Tensor product of linear maps
Linear algebra
13
Trace-duality bound
Linear algebra
12
Diagonal matrix
Linear algebra
40
1
Block-diagonal matrix
Diagonal matrix
23
Triangular matrix
Linear algebra
28
Square root
Algebra
31
Algebraic number
Algebra
18
1
Countability of algebraic numbers
Algebraic number
18
Bezout identity
Algebra
Countable set
Algebra
70
3
Countable union of countable sets
Countable set
12
Cantor pairing function
Countable set
23
Cantor's diagonal argument
Countable set
35
Eigenfunction expansion
Algebra
Field extension
Algebra
155
7
Tower law
Field extension
8
Field compositum
Field extension
47
1
Linearly disjoint field extensions
Field compositum
30
Algebraic closure
Field extension
20
Intermediate field
Field extension
18
Quadratic extension
Field extension
34
Transitivity of algebraic extensions
Field extension
28
Finite field
Algebra
221
4
Multiplicative group of a finite field is cyclic
Finite field
205
3
Finite multiplicative subgroup of a field is cyclic
Multiplicative group of a finite field is cyclic
68
Power roots in a finite field
Multiplicative group of a finite field is cyclic
33
Index-two square-class argument for three related residues
Multiplicative group of a finite field is cyclic
57
Function composition
Algebra
Injective function
Algebra
Irrational number
Algebra
Irrotational vector field
Algebra
Linear recurrence relation
Algebra
74
4
Ordinary generating function of a recurrence
Linear recurrence relation
41
1
Floor-half generating function
Ordinary generating function of a recurrence
11
Affine recurrence
Linear recurrence relation
33
1
Stable affine recurrence
Affine recurrence
18
Linearization
Algebra
13
1
Linearization of a dynamical system
Linearization
Mathematical induction
Algebra
38
2
Strong induction
Mathematical induction
16
Backward induction
Mathematical induction
22
Minimal number of generators
Algebra
Nilpotent polynomial
Algebra
Noetherian ring
Algebra
189
6
Ascending chain condition
Noetherian ring
30
Noetherianity from finite additive rank
Noetherian ring
60
Hilbert basis theorem
Noetherian ring
9
Noetherianity of a quadratic integer order
Noetherian ring
59
1
Nonprincipal ideal in the integers adjoined a square root of minus five
Noetherianity of a quadratic integer order
33
Constant-plus-ideal non-Noetherian subring
Noetherian ring
31
Pauli matrix
Algebra
Pigeonhole principle
Algebra
Polynomial interpolation error
Algebra
14
1
Hermite interpolation
Polynomial interpolation error
14
RSA cryptosystem
Algebra
129
2
Common-modulus RSA attack
RSA cryptosystem
38
RSA private exponent reveals the factorization
RSA cryptosystem
64
Root of unity
Algebra
58
2
Primitive root of unity
Root of unity
13
Root-of-unity filter
Root of unity
23
Smith normal form
Algebra
38
Star-shaped set
Algebra
Surjective function
Algebra
Transcendental number
Algebra
20
1
Liouville number
Transcendental number
20
Unique factorization domain
Algebra
Unit in a ring
Algebra
45
2
Unit group
Unit in a ring
33
1
Multiplicative group of integers modulo n
Unit group
21
Wilson theorem
Algebra
27
Fundamental theorem of algebra
Algebra
19
Group theory
Algebra
3k
113
Group
Group theory
296
15
Finite group
Group
28
1
Order of a finite group
Finite group
12
Nontrivial group
Group
8
Identity element
Group
13
Inverse element
Group
11
Group operation
Group
21
Translation in a group
Group
16
Cyclic group
Group
77
2
Finite subgroup of the multiplicative complex numbers
Cyclic group
28
Generator of a group
Cyclic group
22
Abelian group
Group
16
Finite additive group
Group
31
Subgroup
Group
57
2
Index of a subgroup
Subgroup
14
Index-two subgroup is normal
Subgroup
27
First isomorphism theorem
Group theory
14
Direct product of groups
Group theory
19
Commutator subgroup
Group theory
47
1
Abelianization
Commutator subgroup
21
Center of a group
Group theory
28
1
Cyclic quotient by the center
Center of a group
28
Conjugate subgroup
Group theory
Group action
Group theory
250
11
Conjugation action
Group action
27
1
Normalizer
Conjugation action
10
Orbit-stabilizer theorem
Group action
31
Doubly transitive group action
Group action
26
Symmetry group of a cube
Group action
43
Faithful group action
Group action
70
1
Normal subgroup orbits in a faithful prime-degree action
Faithful group action
54
Orbit of a group action
Group action
8
Stabilizer subgroup
Group action
9
Symmetric group action on subsets
Group action
15
Coset action
Group action
21
Coset
Group theory
111
2
Double coset
Coset
87
1
Sylow subgroup of a subgroup from double cosets
Double coset
48
Lagrange's theorem
Group theory
30
Group embedding
Group theory
94
2
Cayley theorem
Group embedding
75
1
Symmetric-group embedding at one less than the group order
Cayley theorem
56
Generalized dihedral group
Group theory
28
Order of a group element
Group theory
Quotient group
Group theory
General linear group
Group theory
21
Special linear group
Group theory
Group homomorphism
Group theory
55
3
Homomorphism between cyclic groups
Group homomorphism
22
Kernel of a group homomorphism
Group homomorphism
10
Image of a group homomorphism
Group homomorphism
16
Automorphism group
Group theory
16
Finite group theory
Group theory
883
33
Alternating group
Finite group theory
P-group
Finite group theory
Symmetric group
Finite group theory
155
6
Sign homomorphism
Symmetric group
37
Permutation cycle
Symmetric group
63
2
Three-cycle
Permutation cycle
23
Disjoint permutation cycles
Permutation cycle
16
Support of a permutation
Symmetric group
24
Sign of a permutation
Symmetric group
31
Quaternion group
Finite group theory
12
Dicyclic group
Finite group theory
25
Simple group
Finite group theory
70
2
Simplicity of the alternating group A5
Simple group
38
Smallest nonabelian simple group
Simple group
17
General linear group over a finite field
Finite group theory
147
6
Order of a general linear group over a finite field
General linear group over a finite field
10
Upper unitriangular group
General linear group over a finite field
30
Projective general linear group action on the projective line
General linear group over a finite field
79
2
Projective line
Projective general linear group action on the projective line
22
Sylow 2-subgroup of PGL2 over F4
Projective general linear group action on the projective line
37
Special linear group over a finite field
General linear group over a finite field
10
Dihedral group
Finite group theory
25
Sylow theorems
Finite group theory
351
7
Sylow subgroup
Sylow theorems
17
Nonabelian group of order pq
Sylow theorems
34
Conjugation action on Sylow subgroups
Sylow theorems
17
Sylow subgroups of S3, S4 and A5
Sylow theorems
63
Sylow containment from a coset fixed point
Sylow theorems
42
Sylow counts in a faithful degree-seven action with S4 point stabilizers
Sylow theorems
75
Even-involution coset fixed-point lemma
Sylow theorems
67
Cauchy theorem for groups
Finite group theory
61
Composition series
Finite group theory
13
Klein four-group
Finite group theory
15
Torsion element
Group theory
6
Free abelian group
Group theory
23
Normal subgroup
Group theory
37
2
Preimage of a normal subgroup
Normal subgroup
12
Image of a normal subgroup
Normal subgroup
12
Dedekind group
Group theory
12
Projective linear group
Group theory
315
11
Möbius transformation
Projective linear group
286
9
Cross-ratio
Möbius transformation
25
Generalized circle under a Möbius transformation
Möbius transformation
43
Affine subgroup of the Möbius group
Möbius transformation
32
Fixed point of a Möbius transformation
Möbius transformation
81
2
Prescribed fixed points of a Möbius transformation
Fixed point of a Möbius transformation
34
Fixed points of a finite-order Möbius transformation
Fixed point of a Möbius transformation
32
Constant-argument locus of a Möbius transformation
Möbius transformation
27
Classification of Möbius transformations by trace
Möbius transformation
18
Möbius maps commuting with reflection in the unit circle
Möbius transformation
34
Matrix representative of a Möbius transformation
Projective linear group
18
Semidirect product
Group theory
141
4
Affine group over a finite field
Semidirect product
126
3
Affine Galois group of the splitting field of x to the p minus two
Affine group over a finite field
40
Affine semidirect product of cyclic groups of orders eleven and five
Affine group over a finite field
71
1
Conjugacy classes in the affine semidirect product of orders eleven and five
Affine semidirect product of cyclic groups of orders eleven and five
38
Solvable group
Group theory
12
Exponent of a finite group
Group theory
60
1
Finite subgroup of a field multiplicative group is cyclic
Exponent of a finite group
42
Order of an element of a finite group
Group theory
22
Homogeneous polynomial
Algebra
19
Commutative algebra
Algebra
2k
80
Polynomial ring
Commutative algebra
18
Maximal ideal
Commutative algebra
49
1
Maximal ideal quotient criterion
Maximal ideal
19
Local ring
Commutative algebra
38
1
Discrete valuation ring
Local ring
28
Ring
Commutative algebra
297
18
Nilpotent element
Ring
23
Commutative ring
Ring
10
Graded ring
Ring
12
Ideal
Ring
183
10
Generating set of an ideal
Ideal
25
Principal ideal
Ideal
11
Product of ideals
Ideal
17
Intersection of ideals
Ideal
12
Comaximal ideals
Ideal
9
Prime-power ideal
Ideal
17
Ideal approximation theorem
Ideal
16
Reduction modulo an ideal
Ideal
12
Homogeneous ideal
Ideal
28
Radical of an ideal
Ideal
22
Ring homomorphism
Ring
44
2
Evaluation homomorphism
Ring homomorphism
18
First isomorphism theorem for rings
Ring homomorphism
11
Idempotent
Ring
8
Integral domain
Commutative algebra
385
13
Prime element
Integral domain
20
Irreducible element
Integral domain
20
Greatest-common-divisor domain
Integral domain
66
1
Euclid lemma in a greatest-common-divisor domain
Greatest-common-divisor domain
41
Fraction field
Integral domain
21
Principal ideal domain
Integral domain
197
6
Submodule theorem for free modules over a principal ideal domain
Principal ideal domain
35
Euclidean domain
Principal ideal domain
148
4
Euclidean function
Euclidean domain
36
Gaussian integer
Euclidean domain
24
Eisenstein integer
Euclidean domain
75
1
Euclidean norm on the Eisenstein integers
Eisenstein integer
50
BĂ©zout domain
Integral domain
47
Ring product decomposition by an idempotent
Commutative algebra
35
Fiber product of rings
Commutative algebra
16
Unit modulo a prime power
Commutative algebra
18
Nilpotent element modulo a prime power
Commutative algebra
14
Reduction map on unit groups
Commutative algebra
20
Polynomial content
Commutative algebra
134
4
Primitive polynomial
Polynomial content
117
3
Gauss lemma for polynomials
Primitive polynomial
111
2
Polynomial ring over a unique factorization domain
Gauss lemma for polynomials
39
Symmetric rational function in two variables
Gauss lemma for polynomials
52
Eisenstein criterion
Commutative algebra
106
1
Geometric-sum irreducibility criterion
Eisenstein criterion
34
Odd-valuation obstruction to a rational-function square
Commutative algebra
44
Module theory
Commutative algebra
542
21
Primary decomposition theorem for finitely generated modules over a principal ideal domain
Module theory
32
Module over a ring
Module theory
48
1
Submodule
Module over a ring
25
Quotient module
Module theory
19
Free module
Module theory
136
4
Basis of a module
Free module
32
Universal property of a free module
Free module
29
Rank of a free module
Free module
23
Invariant basis number for a commutative ring
Free module
29
Torsion-free module
Module theory
19
Projective module
Module theory
38
1
Free modules are projective
Projective module
18
Cyclic module
Module theory
12
Irreducible module
Module theory
41
1
Simple module over a commutative ring
Irreducible module
25
Annihilator of a module
Module theory
15
Structure theorem for finitely generated modules over a principal ideal domain
Module theory
166
4
Finitely generated torsion-free module over a principal ideal domain
Structure theorem for finitely generated modules over a principal ideal domain
85
1
Classification of integral matrices satisfying the third cyclotomic polynomial
Finitely generated torsion-free module over a principal ideal domain
57
Elementary divisor
Structure theorem for finitely generated modules over a principal ideal domain
19
Indecomposable finite abelian groups
Structure theorem for finitely generated modules over a principal ideal domain
42
Prime ideal
Commutative algebra
55
1
Prime ideal quotient criterion
Prime ideal
31
Boolean ring
Commutative algebra
53
1
Prime ideals of a Boolean ring are maximal
Boolean ring
37
Coefficientwise quotient of a polynomial ring
Commutative algebra
24
Irreducible real polynomial
Commutative algebra
15
Kummer irreducibility criterion
Commutative algebra
29
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