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Words: 5k
Articles: 228
Table of contents
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
Ancestors
(4)
Algebra
Area of mathematics
Mathematics
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