MATLAB Function Reference |

**Syntax**

**Description**

The `rank`

function provides an estimate of the number of linearly independent rows or columns of a full matrix.

returns the number of singular values of ```
k = rank(A)
```

`A`

that are larger than the default tolerance, `max(size(A))*norm(A)*eps`

.

returns the number of singular values of `k = rank(A,`

tol```
)
```

`A`

that are larger than `tol`

.

**Remark**

Use `sprank`

to determine the structural rank of a sparse matrix.

**Algorithm**

There are a number of ways to compute the rank of a matrix. MATLAB uses the method based on the singular value decomposition, or SVD. The SVD algorithm is the most time consuming, but also the most reliable.

**See Also**

**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.

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