numpy (matrix solver) - python vs. matlab

[Russ P.]

On May 1, 4:05 pm, Paul Rubin <no.em... at nospam.invalid> wrote:
> someone <newsbo... at gmail.com> writes:
> > Actually I know some... I just didn't think so much about, before
> > writing the question this as I should, I know theres also something
> > like singular value decomposition that I think can help solve
> > otherwise illposed problems,
>
> You will probably get better advice if you are able to describe what
> problem (ill-posed or otherwise) you are actually trying to solve.  SVD
> just separates out the orthogonal and scaling parts of the
> transformation induced by a matrix.  Whether that is of any use to you
> is unclear since you don't say what you're trying to do.

I agree with the first sentence, but I take slight issue with the word
"just" in the second. The "orthogonal" part of the transformation is
non-distorting, but the "scaling" part essentially distorts the space.
At least that's how I think about it. The larger the ratio between the
largest and smallest singular value, the more distortion there is. SVD
may or may not be the best choice for the final algorithm, but it is
useful for visualizing the transformation you are applying. It can
provide clues about the quality of the selection of independent
variables, state variables, or inputs.