Search Results for ""

If all the eigenvalues of a real matrix A have real parts, then to an arbitrary negative definite quadratic form (x,Wx) with x=x(t) there corresponds a positive definite ...

Denote the sum of two matrices A and B (of the same dimensions) by C=A+B. The sum is defined by adding entries with the same indices c_(ij)=a_(ij)+b_(ij) over all i and j. ...

Matrix decomposition refers to the transformation of a given matrix (often assumed to be a square matrix) into a given canonical form.

The matrix direct sum of n matrices constructs a block diagonal matrix from a set of square matrices, i.e., direct sum _(i=1)^nA_i = diag(A_1,A_2,...,A_n) (1) = [A_1 ; A_2 ; ...

The process of computing a matrix inverse.

The power A^n of a matrix A for n a nonnegative integer is defined as the matrix product of n copies of A, A^n=A...A_()_(n). A matrix to the zeroth power is defined to be the ...

The result of a matrix multiplication.

The rank of a matrix or a linear transformation is the dimension of the image of the matrix or the linear transformation, corresponding to the number of linearly independent ...

A real, nondegenerate n×n symmetric matrix A, and its corresponding symmetric bilinear form Q(v,w)=v^(T)Aw, has signature (p,q) if there is a nondegenerate matrix C such that ...

The eigenvalues of a matrix A are called its spectrum, and are denoted lambda(A). If lambda(A)={lambda_1,...,lambda_n}, then the determinant of A is given by ...