rank

Arguments

X

real or complex matrix

tol

nonnegative real number

Description

rank(X) is the numerical rank of X i.e. the number of singular values of X that are larger than norm(size(X),'inf') * norm(X) * %eps.

rank(X,tol) is the number of singular values of X that are larger than tol.

rank([]) returns 0.

The default value of tol is proportional to norm(X). As a consequence rank([1.d-80,0;0,1.d-80]) is 2 !.

Examples

rank([1.d-80,0;0,1.d-80])
rank([1,0;0,1.d-80])

See also

• svd — singular value decomposition
• qr — QR decomposition
• rowcomp — row compression, range
• colcomp — column compression, kernel, nullspace
• lu — LU factorization with pivoting