Search results
Results from the WOW.Com Content Network
An exchange matrix is the simplest anti-diagonal matrix. Any matrix A satisfying the condition AJ = JA is said to be centrosymmetric. Any matrix A satisfying the condition AJ = JA T is said to be persymmetric. Symmetric matrices A that satisfy the condition AJ = JA are called bisymmetric matrices. Bisymmetric matrices are both centrosymmetric ...
Cuthill-McKee ordering of a matrix RCM ordering of the same matrix. In numerical linear algebra, the Cuthill–McKee algorithm (CM), named after Elizabeth Cuthill and James McKee, [1] is an algorithm to permute a sparse matrix that has a symmetric sparsity pattern into a band matrix form with a small bandwidth.
For example, to solve a system of n equations for n unknowns by performing row operations on the matrix until it is in echelon form, and then solving for each unknown in reverse order, requires n(n + 1)/2 divisions, (2n 3 + 3n 2 − 5n)/6 multiplications, and (2n 3 + 3n 2 − 5n)/6 subtractions, [10] for a total of approximately 2n 3 /3 operations.
In linear algebra, an invertible matrix is a square matrix that has an inverse. In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the operation. An invertible matrix multiplied by its inverse yields the identity matrix. Invertible matrices are the same size as their ...
The direct-quadrature-zero (DQZ, DQ0 [1] or DQO, [2] sometimes lowercase) or Park transformation (named after Robert H. Park) is a tensor that rotates the reference frame of a three-element vector or a three-by-three element matrix in an effort to simplify analysis.
Furthermore, the product of an anti-diagonal matrix with a diagonal matrix is anti-diagonal, as is the product of a diagonal matrix with an anti-diagonal matrix. An anti-diagonal matrix is invertible if and only if the entries on the diagonal from the lower left corner to the upper right corner are nonzero. The inverse of any invertible anti ...
In mathematics, specifically linear algebra, the Woodbury matrix identity – named after Max A. Woodbury [1] [2] – says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix.
If A is an m × n matrix and A T is its transpose, then the result of matrix multiplication with these two matrices gives two square matrices: A A T is m × m and A T A is n × n. Furthermore, these products are symmetric matrices. Indeed, the matrix product A A T has entries that are the inner product of a row of A with a column of A T.