Hi John,
On 2016-10-27, John H Palmieri <jhpalmier...@gmail.com> wrote:
> (1) Why should a nonsquare matrix even have an "is_similar" method? Can we
> get rid of that? (Same for "determinant" and some other methods.)
It would be possible using the category framework's "ElementMethods".
x.is_similar(y) makes sense for any monoid ("there is an invertible element p
such that px=yp"), so we can define it on the category level. The method would
rely on a method x._similarity_witness(y), which is supposed to return either
an appropriate element p, or None if there is none, or NotImplemented (resp.
result in an attribute error) when we are in a monoid where we can not
effectively
test whether two elements are similar.
That approach would give what you stated, as square matrices are in the
category of monoids, whereas non-square matrices aren't.
Best regards,
Simon
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