# Documentation

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# rank

Rank of matrix

## Syntax

`k = rank(A)k = rank(A,tol)`

## Description

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

`k = rank(A)` returns the number of singular values of `A` that are larger than the default tolerance, `max(size(A))*eps(norm(A))`.

`k = rank(A,tol)` returns the number of singular values of `A` that are larger than `tol`.

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### Tips

Use `sprank` to determine the structural rank of a sparse matrix.

### Algorithms

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

The `rank` algorithm is

```s = svd(A); tol = max(size(A))*eps(max(s)); r = sum(s > tol);```