[Numpy-discussion] How to solve homogeneous linear equations with NumPy?
Charles R Harris
Fri Dec 4 09:52:52 CST 2009
On Fri, Dec 4, 2009 at 2:09 AM, David Goldsmith <email@example.com>wrote:
> On Thu, Dec 3, 2009 at 9:17 AM, Charles R Harris <
> firstname.lastname@example.org> wrote:
>> On Thu, Dec 3, 2009 at 7:59 AM, Peter Cai <email@example.com> wrote:
>>> Thanks, I've read some explanations on wikipedia and finally found out
>>> how to solve homogeneous equations by singular value decomposition.
>> Note that the numpy svd doesn't quite conform to what you will see in
>> those sources and the documentation is confusing. Numpy returns
>> u,s,v and a = u*diag(s)*v, whereas the decomposition is normally written
>> as u*diag(s)*v^T, i.e., the numpy v is the transpose (Hermitean conjugate)
>> of the conventional v.
> It's quite clear to me (at least in the version of the doc in the Wiki)
> that what is returned in the third "slot" is the "Hermitean of v", i.e., the
> third factor in the decomposition the way it is "normally written"; how
> would you suggest it be made clearer?
Leave off the Hermitean bit since it is irrelevant to our decomposition,
show a = u*diag(s)*v, and make a note explaining the usual convention.
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