fullrf

full rank factorization

Calling Sequence

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

Arguments

: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 singular value decomposition
• qr QR decomposition
• fullrfk full rank factorization of A^k
• rowcomp row compression, range
• colcomp column compression, kernel, nullspace