COND

Purpose:

Estimates the condition number of a matrix.

COND(a, p)

a	-	The input matrix.
p	-	Optional. An integer, the p-norm. Defaults to 2, singular value method.

A real, the estimated condition number.

W1: {{1, 2, 3},

{4, 5, 6},

{7, 8, 9}}

W2: {{1, 2, 3},

{4, 5, 6},

{7, 8, 0}}

cond(W1) == 8.579581E+016

cond(W2) == 35.105870

By default, COND uses SVD to compute the singular values of a matrix. The result is the ratio of the maximum and minimum singular values.

If p is specified, the condition number is computed as:

c = norm(a, p) * norm(inv(a), p)

The condition number is infinite for a singular matrix, thus a large condition number indicates an ill conditioned matrix.

See RCOND to estimate of the reciprocal condition number.