#7522: Implement orthogonal complement in vector spaces
-------------------------------------------------+--------------------------
Reporter: kcrisman | Owner: was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.11
Component: linear algebra | Resolution:
Keywords: sd48 | Work issues:
Report Upstream: N/A | Reviewers: Karl-Dieter
Crisman, Nils Bruin
Authors: Jason Grout, Travis Scrimshaw | Merged in:
Dependencies: | Stopgaps:
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Old description:
> It should be easy to get the orthogonal complement of a subspace W of a
> vector space V. From Jason Grout:
> {{{
> sage: def orthogonal_complement(space):
> ....: if space.dimension()==0:
> ....: return space.ambient_vector_space()
> ....: else:
> ....: return space.basis_matrix().right_kernel()
> }}}
> One would also want to add an option to specify the larger space in which
> you were dealing, with it defaulting to the ambient vector space.
> Probably 'perp()' should be an alias.
>
> ----
>
> Apply: [attachment: trac_7522-perp-ts.patch]
New description:
It should be easy to get the orthogonal complement of a subspace W of a
vector space V. From Jason Grout:
{{{
sage: def orthogonal_complement(space):
....: if space.dimension()==0:
....: return space.ambient_vector_space()
....: else:
....: return space.basis_matrix().right_kernel()
}}}
One would also want to add an option to specify the larger space in which
you were dealing, with it defaulting to the ambient vector space.
Probably 'perp()' should be an alias.
----
Apply: [attachment: trac_7522-perp-ts.patch] and
[attachment:trac_7522-finite.patch]
--
Comment (by kcrisman):
Okay, Travis and/or Nils and/or anyone else, is this okay? The
terminology is really the issue here, but hopefully this will satisfy
everyone.
Patchbot, apply trac_7522-perp-ts.patch and trac_7522-finite.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7522#comment:20>
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