cond

Arguments

X

real or complex matrix. If c = cond(X, p), X must be real or complex square matrix.

p

scalar or string (type of norm) (default value = 2).

c

real scalar, the condition number.

Description

c = cond(X)

returns condition number in 2-norm.cond(X) is the ratio of the largest singular value of X to the smallest.

c = cond(X, p)

returns condition number in p-norm : norm(X, p) * norm(inv(X), p). If p is specified, p can be equal to :

• p = 1. cond(X, p) returns condition number in 1-norm.

• p = 2. cond(X, p) returns condition number in 2-norm.

• p = %inf or 'inf'. cond(X, p) returns condition number in infinity norm.

• p = 'fro'. cond(X, p) returns condition number in Frobenius norm.

Examples

A=testmatrix('hilb',6);
// condition number in 2-norm
cond(A)
cond(A, 2)

// condition number in 1-norm
cond(A, 1)

// condition number in infinity norm
cond(A, %inf)

// condition number in Frobenius norm
cond(A, 'fro')

See also

• rcond — inverse condition number
• svd — singular value decomposition
• norm — norms of a vector or a matrix

History

X = [1 0; 1 -1; 0 1];
cond(X)

X = [1 -6 0; 1 0 -4;1 0 2];
cond(X, 1) // condition number in 1-norm (p = 1)