MATLAB Function Reference

rank

Rank of a 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))*norm(A)*eps.

k = rank(A,tol) returns the number of singular values of 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.

The rank algorithm is

• s = svd(A);
  tol = max(size(A))*s(1)*eps;
  r = sum(s > tol);
  

See Also

sprank

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.

randperm

rat, rats