associated with that eigenvalue. By the definition of eigenvalues and eigenvectors, γT(λ) ≥ 1 because every eigenvalue has at least one eigenvector. The eigenspaces...
102 KB (13,609 words) - 13:41, 19 December 2024
designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors. Given an n × n...
40 KB (4,867 words) - 05:54, 21 December 2024
Eigendecomposition of a matrix (redirect from Inverse eigenvalues theorem)
canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way....
40 KB (5,590 words) - 15:14, 28 October 2024
{\displaystyle x\in [0,L]} , the following are the eigenvalues and normalized eigenvectors. The eigenvalues are ordered in descending order. λ j = − j 2 π...
11 KB (2,781 words) - 16:17, 8 April 2022
perturbation of a simple eigenvalue (see in multiplicity of eigenvalues). In the entry applications of eigenvalues and eigenvectors we find numerous scientific...
27 KB (6,234 words) - 06:29, 21 December 2024
Linear algebra (redirect from Double eigenvalue)
matrix (or of the endomorphism), and there are, at most, n eigenvalues. If a basis exists that consists only of eigenvectors, the matrix of f on this basis...
67 KB (7,983 words) - 21:05, 12 December 2024
Quantum state (redirect from Introduction to eigenvalues and eigenvectors)
momentum of 1 kg⋅m/s if and only if one of the eigenvalues of the momentum operator is 1 kg⋅m/s. The corresponding eigenvector (which physicists call an...
41 KB (5,503 words) - 11:41, 16 December 2024
necessary for the eigenvalues and the components of the eigenvectors to have complex values. The set spanned by all generalized eigenvectors for a given λ...
38 KB (7,052 words) - 13:49, 4 October 2024
Pauli matrices (section Eigenvectors and eigenvalues)
}}_{k}+1\right)~.} Its eigenvalues are therefore 1 or −1. It may thus be utilized as an interaction term in a Hamiltonian, splitting the energy eigenvalues of its symmetric...
45 KB (7,414 words) - 14:18, 14 December 2024
Square matrix (section Eigenvalues and eigenvectors)
every vector is expressible as a linear combination of eigenvectors. In both cases, all eigenvalues are real. A symmetric n×n-matrix is called positive-definite...
16 KB (1,831 words) - 00:24, 24 September 2024
for example, a square matrix is invertible if and only if it has a nonzero determinant and the eigenvalues of a square matrix are the roots of a polynomial...
108 KB (13,482 words) - 09:37, 15 December 2024
produces a response y(t) = λf(t), where λ is a complex scalar eigenvalue. Eigenvalues and eigenvectors Hilbert–Schmidt theorem Spectral theory of ordinary differential...
17 KB (2,347 words) - 07:05, 16 December 2024
linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix...
28 KB (4,679 words) - 05:34, 21 December 2024
Perron–Frobenius theorem (redirect from Perron–Frobenius eigenvector)
except positive multiples of v (respectively, left eigenvectors except ww'w), i.e., all other eigenvectors must have at least one negative or non-real component...
58 KB (8,238 words) - 15:02, 19 November 2024
Second derivative (category Functions and mappings)
formulas for eigenvalues and eigenvectors of the second derivative can be obtained. For example, assuming x ∈ [ 0 , L ] {\displaystyle x\in [0,L]} and homogeneous...
15 KB (2,013 words) - 08:18, 28 August 2024
algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix. The QR algorithm was...
26 KB (4,080 words) - 13:55, 2 December 2024
fixed points can be analyzed by determining their respective eigenvalues and eigenvectors. Beginning with the Jacobian: ( 0 − 1 − 1 1 a 0 z 0 x − c ) {\displaystyle...
24 KB (3,602 words) - 15:53, 8 September 2024
is an eigenvalue algorithm and an important example of an iterative method. Arnoldi finds an approximation to the eigenvalues and eigenvectors of general...
13 KB (1,842 words) - 09:21, 30 May 2024
Phase plane (section Eigenvectors and nodes)
and λ2 are the eigenvalues, and (k1, k2), (k3, k4) are the basic eigenvectors. The constants c1 and c2 account for the nonuniqueness of eigenvectors and...
9 KB (1,231 words) - 06:52, 20 April 2024
extends eigenvalues and eigenvectors to linear operators on Hilbert space, and more generally to the elements of a Banach algebra In nuclear and particle...
1 KB (201 words) - 23:03, 5 June 2022
Arrowhead matrix (section Eigenvalues and eigenvectors)
arrowhead matrices are used in some algorithms for finding of eigenvalues and eigenvectors. Let A be a real symmetric (permuted) arrowhead matrix of the...
7 KB (1,329 words) - 21:23, 6 March 2024
Vector space (redirect from Vectors and Scalars)
all eigenvectors corresponding to a particular eigenvalue of f forms a vector space known as the eigenspace corresponding to the eigenvalue (and f) in...
87 KB (11,491 words) - 19:32, 22 December 2024
Adjacency matrix (section Isomorphism and invariants)
adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory...
20 KB (2,459 words) - 00:58, 16 December 2024
general eigenvectors is known. Moreover, the eigenvectors are not unique because any linear combination of eigenvectors for the same eigenvalue is also...
76 KB (12,311 words) - 10:11, 15 December 2024
{\displaystyle m} "most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an n × n {\displaystyle n\times n} Hermitian matrix, where...
43 KB (8,287 words) - 09:57, 15 May 2024
which we can use an eigenvalue algorithm. It is used in all applications that involve approximating eigenvalues and eigenvectors, often under different...
33 KB (5,732 words) - 14:05, 6 October 2024
Voigt effect (section Eigenvalues and eigenvectors)
effective dielectric tensor from which one calculates systems eigenvalues and eigenvectors. As usual, from this tensor, magneto-optical phenomena are described...
18 KB (3,530 words) - 19:59, 14 December 2024
quadratic eigenvalue problem (QEP), is to find scalar eigenvalues λ {\displaystyle \lambda } , left eigenvectors y {\displaystyle y} and right eigenvectors x...
5 KB (999 words) - 11:35, 20 September 2023
consisting of eigenvectors of T {\displaystyle T} , and the diagonal entries of D {\displaystyle D} are the corresponding eigenvalues of T {\displaystyle...
27 KB (4,693 words) - 14:00, 9 December 2024
graph into eigenvalues and eigenvectors. Analogously to the classical Fourier transform, the eigenvalues represent frequencies and eigenvectors form what...
12 KB (1,845 words) - 20:01, 8 November 2024