fullrf - full rank factorization

Calling Sequence

[Q,M,rk]=fullrf(A,[tol])

Parameters

• A : real or complex matrix
• tol : real number (threshold for rank determination)
• Q,M : real or complex matrix
• rk : integer (rank of A)

Description

Full rank factorization : fullrf returns Q and M such that A = Q*M with range(Q)=range(A) and ker(M)=ker(A), Q full column rank , M full row rank, rk = rank(A) = #columns(Q) = #rows(M).

tol is an optional real parameter (default value is sqrt(%eps)). The rank rk of A is defined as the number of singular values larger than norm(A)*tol.

If A is symmetric, fullrf returns M=Q'.

Examples

A=rand(5,2)*rand(2,5);
[Q,M]=fullrf(A);
norm(Q*M-A,1)
[X,d]=rowcomp(A);Y=X';
svd([A,Y(:,1:d),Q])        //span(Q) = span(A) = span(Y(:,1:2))
 

See Also

svd  qr  fullrfk  rowcomp  colcomp  

Author

F.D.;