fullrf

Scilab Function
Last update : 16/12/2004

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.;