Search Results for ""

A square matrix A such that the matrix power A^(k+1)=A for k a positive integer is called a periodic matrix. If k is the least such integer, then the matrix is said to have ...

If all elements a_(ij) of an irreducible matrix A are nonnegative, then R=minM_lambda is an eigenvalue of A and all the eigenvalues of A lie on the disk |z|<=R, where, if ...

If mu=(mu_1,mu_2,...,mu_n) is an arbitrary set of positive numbers, then all eigenvalues lambda of the n×n matrix a=a_(ij) lie on the disk |z|<=m_mu, where ...

An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of {1,...,n} into pairs of elements. The Pfaffian is the square root of ...

The element in the diagonal of a matrix by which other elements are divided in an algorithm such as Gauss-Jordan elimination is called the pivot element. Partial pivoting is ...

A matrix whose entries are polynomials.

A positive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a positive number, i.e., a_(ij)>0 for all i, j. Positive matrices are therefore a ...

A real matrix is a matrix whose elements consist entirely of real numbers. The set of m×n real matrices is sometimes denoted R^(m×n) (Zwillinger 1995, p. 116).

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...

A right eigenvector is defined as a column vector X_R satisfying AX_R=lambda_RX_R. In many common applications, only right eigenvectors (and not left eigenvectors) need be ...