# cond

Condition number with respect to inversion

## Syntax

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

## Description

The condition number of a matrix measures the sensitivity of the solution of a system of linear equations to errors in the data. It gives an indication of the accuracy of the results from matrix inversion and the linear equation solution. Values of `cond(X)` and `cond(X,p)` near 1 indicate a well-conditioned matrix.

`c = cond(X)` returns the 2-norm condition number, the ratio of the largest singular value of `X` to the smallest.

`c = cond(X,p)` returns the matrix condition number in `p`-norm:

`norm(X,p) * norm(inv(X),p)`

If p is...

Then cond(X,p) returns the...

1

1-norm condition number

2

2-norm condition number

'fro'

Frobenius norm condition number

inf

Infinity norm condition number

collapse all

### Algorithms

The algorithm for `cond` (when ```p = 2```) uses the singular value decomposition, `svd`. When the input matrix is sparse, `cond` ignores any specified `p` value and calls `condest`.