cond (MATLAB Functions)

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
```
 


 
```

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