# Documentation

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# rank

Rank of matrix

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.

## 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);