In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices...
17 KB (2,466 words) - 02:48, 13 May 2024
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...
27 KB (4,725 words) - 03:32, 17 June 2024
anti-diagonal (sometimes Harrison diagonal, secondary diagonal, trailing diagonal, minor diagonal, off diagonal or bad diagonal). An n-by-n matrix A is...
4 KB (510 words) - 22:02, 15 March 2024
A block diagonal matrix is a block matrix that is a square matrix such that the main-diagonal blocks are square matrices and all off-diagonal blocks are...
29 KB (4,768 words) - 15:57, 12 August 2024
tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal (the first diagonal below this)...
18 KB (2,704 words) - 06:08, 29 August 2024
spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix A satisfying the equation...
13 KB (1,656 words) - 01:07, 5 June 2024
the main diagonal of a square matrix. They lie on the imaginary line which runs from the top left corner to the bottom right corner of the matrix. For instance...
16 KB (1,831 words) - 06:07, 16 June 2024
Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of...
17 KB (2,812 words) - 05:04, 29 August 2024
where Q is the square n × n matrix whose ith column is the eigenvector qi of A, and Λ is the diagonal matrix whose diagonal elements are the corresponding...
40 KB (5,589 words) - 01:55, 2 September 2024
equivalent conditions. M {\displaystyle \ M\ } is congruent with a diagonal matrix with positive real entries. M {\displaystyle \ M\ } is symmetric...
50 KB (8,587 words) - 00:21, 23 August 2024