rank

Numerical rank of a matrix.

Syntax

r = rank(A)
r = rank(A, tol)

Description

Returns the numerical rank of A — the number of singular values that exceed the tolerance tol. The default tolerance is max(size(A)) * eps(norm(A)).

The optional ref reference flag and tol are MathJet extensions that pass tolerance information through; for compatibility with MATLAB’s two-argument form, pass tolerance as the second argument.

Examples

rank([1 2; 2 4])         % 1   (linearly dependent rows)
rank(magic(3))           % 3
rank(magic(4))           % 3   (magic(4) is rank-deficient)

See also

• null — Orthonormal basis for the null space of a matrix.
• svd — Singular value decomposition.
• cond — Condition number of a matrix.