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Справка Scilab >> Linear Algebra > Kernel > fullrf

# fullrf

full rank factorization

### Syntax

`[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))```

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