Re: Full rank factorization

On Aug 13, 7:41 pm, "Aelover11" <aelove...@xxxxxxxxx> wrote:
Anybody knows? Please help!!! thanks/

"Aelover11" <aelove...@xxxxxxxxx> wrote in message

news:f9pq6d$48e$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Hi all,

I forget this basic method in algebra, please tell me the steps to full
rank factorize a matrix.

specifically, I have a m x n matrix A with rank = r, r<mimn(m,n), I need
to obtain B (mxr) and C (rxn)such that
A=BC/

Thanks

Use Gaussian elimination to express A as a product
of elementary matrices E times a row echelon matrix
R. Note E is mxm and R is mxn (since A is mxn).

Since all but the first r rows of R are zeros,
we may rewrite A = E * R as A = B * C by simply
dropping the final m-r rows of R to get C and
correspondingly the final m-r columns of E to get
B. Now B is mxr and C is rxn.

regards, chip

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