linear algebra, a square matrix A {\displaystyle A} is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists... 23 KB (4,044 words) - 13:36, 12 April 2024 |
rotation matrices. A method for finding log A for a diagonalizable matrix A is the following: Find the matrix V of eigenvectors of A (each column of V is an... 17 KB (2,931 words) - 18:43, 9 May 2024 |
there exists a unitary matrix U such that UAU* and UBU* are diagonal matrices. In other words A and B are simultaneously diagonalizable. In this special case... 13 KB (1,630 words) - 22:34, 6 December 2023 |
decomposition) of a diagonalizable matrix is a decomposition of a diagonalizable matrix into a specific canonical form whereby the matrix is represented in... 4 KB (510 words) - 22:01, 12 July 2022 |
diagonal entries of a matrix. Anti-diagonal matrix Banded matrix Bidiagonal matrix Diagonally dominant matrix Diagonalizable matrix Jordan normal form Multiplication... 17 KB (2,465 words) - 23:13, 1 December 2023 |
factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can... 36 KB (4,968 words) - 11:38, 28 February 2024 |
Spectral theorem (category Matrix theory) computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. The concept of diagonalization... 24 KB (3,618 words) - 14:59, 26 April 2024 |
nilpotent matrix are always zero. Consequently, a nilpotent matrix cannot be invertible. The only nilpotent diagonalizable matrix is the zero matrix. See also:... 10 KB (1,934 words) - 18:44, 10 March 2024 |
Unipotent (redirect from Unipotent matrix) quasi-unipotent means that some power is unipotent, for example for a diagonalizable matrix with eigenvalues that are all roots of unity. In the theory of algebraic... 11 KB (1,815 words) - 08:42, 20 January 2023 |
contradict what is said on simultaneous diagonalization in the article Diagonalizable matrix, which refers to simultaneous diagonalization by a similarity transformation... 47 KB (8,431 words) - 10:11, 10 April 2024 |
where D is a diagonal matrix and V is a suitable invertible matrix. If A can be written in this form, it is called diagonalizable. More generally, and... 106 KB (13,106 words) - 15:41, 8 May 2024 |
P is the minimal polynomial of A. We further assume that A is a diagonalizable matrix. In particular, the roots of P are simple, and the "interpolation"... 55 KB (10,407 words) - 09:28, 13 November 2023 |
Commuting matrices (category Matrix theory) {\displaystyle AB=BA} ) if they are simultaneously diagonalizable (that is, there exists an invertible matrix P {\displaystyle P} such that both P − 1 A P {\displaystyle... 9 KB (1,390 words) - 04:09, 29 October 2023 |
algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an... 4 KB (576 words) - 15:39, 14 February 2024 |
known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix A {\displaystyle A} , the algorithm will produce a number λ {\displaystyle... 13 KB (2,497 words) - 01:35, 5 December 2023 |
matrix B. For example, A is called diagonalizable if it is similar to a diagonal matrix. Not all matrices are diagonalizable, but at least over the complex... 8 KB (1,081 words) - 22:27, 10 April 2024 |
Projection (linear algebra) (section Projection matrix) vector space of dimension d {\displaystyle d} over a field is a diagonalizable matrix, since its minimal polynomial divides x 2 − x {\displaystyle x^{2}-x}... 34 KB (5,802 words) - 21:53, 28 April 2024 |
C(p)} is diagonalizable as C ( p ) = V − 1 D V {\displaystyle C(p)=V^{-1}\!DV} , where D is the diagonal matrix and V is the Vandermonde matrix corresponding... 11 KB (2,443 words) - 18:51, 30 January 2024 |
positive-semidefinite matrix Pfaffian Projection Spectral theorem Perron–Frobenius theorem List of matrices Diagonal matrix, main diagonal Diagonalizable matrix Triangular... 5 KB (377 words) - 12:12, 30 October 2023 |
Vitold Belevitch (section Scattering matrix) version only applied to systems that could be represented by a diagonalizable matrix. The test was subsequently generalised by Vasile M. Popov (in 1966)... 27 KB (3,346 words) - 23:12, 1 May 2024 |
∗ {\displaystyle U^{*}U=UU^{*}} ). U is diagonalizable; that is, U is unitarily similar to a diagonal matrix, as a consequence of the spectral theorem... 10 KB (1,307 words) - 18:43, 5 May 2024 |
diagonalization procedure. A diagonalizable matrix is similar, in fact, to a special case of Jordan matrix: the matrix whose blocks are all 1 × 1. More... 16 KB (2,805 words) - 15:21, 20 January 2024 |
general (complex) symmetric matrix may be defective and thus not be diagonalizable. If A {\displaystyle A} is diagonalizable it may be decomposed as A =... 17 KB (2,823 words) - 17:24, 20 March 2024 |
The matrix function f ( X ) {\displaystyle f(\mathbf {X} )} is defined in terms of the scalar function f ( x ) {\displaystyle f(x)} for diagonalizable matrices... 85 KB (7,035 words) - 06:09, 18 April 2024 |
square matrix A is diagonalizable, if there is an invertible matrix P such that D = P − 1 A P {\displaystyle D=P^{-1}\,A\,P} is a diagonal matrix, that... 12 KB (2,146 words) - 16:04, 13 January 2024 |
List of named matrices (redirect from List of matrix) matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries... 31 KB (1,336 words) - 00:12, 30 November 2023 |
the algebra, i.e., to there being simultaneously diagonalizable matrices (see diagonalizable matrix). If G is group with Lie algebra g {\displaystyle... 21 KB (3,258 words) - 12:23, 1 March 2024 |
an abstract element of an algebraic structure that generalizes a diagonalizable matrix. A precise meaning depends on context: A semisimple element in the... 457 bytes (95 words) - 06:54, 13 August 2022 |
a complex-valued diagonalizable matrix. In its substance, it states an absolute upper bound for the deviation of one perturbed matrix eigenvalue from a... 9 KB (1,640 words) - 08:09, 19 March 2022 |