# cond

condition number

## Calling Sequence

                c = cond(X)
                c = cond(X, p)

## 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
- svd
- norm

## History

5.4.0

Calling `cond(X)`, where `X` is non square matrix, is now managed. For example:

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

Calling `cond(X, p)` allows to calculate p-norm condition number. For example:

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