MATLAB Function Reference  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
```

```

Algorithm

The algorithm for `cond` (when `p = 2`) uses the singular value decomposition, `svd`.

See Also

`condeig`, `condest`, `norm`, `normest`, `rank`, `rcond`, `svd`

References

  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.

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