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fullrf(1) Scilab Function fullrf(1)
NAME
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'.
EXAMPLE
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.
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