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Words: 2k
Articles: 76
Linear operator theory studies
linear maps
, their
spectra
, invariant subspaces, and normal forms.
Table of contents
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
Ancestors
(5)
Linear algebra
Algebra
Area of mathematics
Mathematics
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