#7522: Implement orthogonal complement in vector spaces
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Reporter: kcrisman | Owner: was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.9
Component: linear algebra | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers: Karl-Dieter
Crisman
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.
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]
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Comment (by tscrim):
For patchbot:
Apply: trac_7522-perp-ts.patch
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7522#comment:8>
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