MATLAB Function Reference |

Condition number with respect to inversion

**Syntax**

**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

**Algorithm**

The algorithm for `cond`

(when `p = 2`

) uses the singular value decomposition, `svd`

.

**See Also**

`condeig`

, `condest`

, `norm`

, `normest`

, `rank`

, `rcond`

, `svd`

**References**

[1] Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra,
J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen,
*LAPACK User's Guide* (http://www.netlib.org/lapack/lug/
lapack_lug.html), Third Edition, SIAM, Philadelphia, 1999.

computer | condeig |

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