DADiSP Worksheet Functions > Function Categories > Matrix Math and Special Matrices > COND

 

COND

Purpose:

Estimates the condition number of a matrix.

Syntax:

COND(a, p)

a

-

The input matrix.

p

-

Optional. An integer, the p-norm. Defaults to 2, singular value method.

Returns:

A real, the estimated condition number.

Example:

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

Remarks:

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.

See Also:

NORM

RANK

RCOND

SVD