Scilab 6.0.0

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# 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'`

.

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