numpy (matrix solver) - python vs. matlab

[someone]

On 05/02/2012 01:38 AM, Russ P. wrote:
> 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.

Me would like to hear more! :-)

It would really appreciate if anyone could maybe post a simple SVD 
example and tell what the vectors from the SVD represents geometrically 
/ visually, because I don't understand it good enough and I'm sure it's 
very important, when it comes to solving matrix systems...