Re: PSeudoinvers Matrices

On Jun 17, 5:14 am, Gordon Sande <g.sa...@xxxxxxxxxxxxxxxx> wrote:
On 2009-06-17 02:23:49 -0300, GagoX <elgrang...@xxxxxxxxx> said:

Thanx again Greg for the reply...

firstly, I think my problem (equation W*X=R) has nothing to do with R
but just with W.

Let me explain myself.
doing what you tell me, getting the RHS of W'Wx=W'r gives me the
columns of X=inv(W'W)*W'R

The "normal equations" of least squares.

but using this solution on the original problem does not work because
W*inv(W'W)*W'R is not equal to R!

The pseudoinverses gives solutions to overdetermined equations in the sense
of least squares. If you paid close attention to the words your would have
noticed that "solution" and "over determined" do not get along very well
until some additional adjectives like "in the sense of least squares"
are added.

I going crazy here...everything seemed to be so easy when  working with
square matrices...but rectangular ones...uuuff. :-)

Just generalize to allow for least squares solutions.

Thanx Again!



Layman's approach. Let s denote minimum of m,n. Convert each matrix
to an sxs matrix by truncating on the right and the bottom. Identify
all possible matrices Y that solve this
matrix. If original problem is solvable, then upper left portion of X
must = one of the
matrices Y.

I never studied matrix theory; this is simply my intuition.
.

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