#15245: Pfaffian of a skew-symmetric matrix
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Reporter: darij | Owner:
Type: enhancement | Status:
Priority: major | positive_review
Component: combinatorics | Milestone: sage-5.13
Keywords: matrix, sage-combinat, | Resolution:
pfaffian | Merged in:
Authors: Darij Grinberg | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #14117 | Stopgaps:
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Comment (by nbruin):
Replying to [comment:4 darij]:
> thanks once again for the reviews! I fixed all of your issues apart from
not using {{{is_skew_symmetric()}}} because that method doesn't check
diagonal entries to be 0 (it only checks them to satisfy x = -x, which is
not the same in characteristic 2):
I think that's the definition of skew symmetric/antisymmetric: that
A^T^=-A. It just happens to be the case that the concepts "symmetric" and
"antisymmetric" coincide in characteristic 2.
In other words: skew symmetric matrices don't have to have 0 on their
diagonal. Note that the terminology comes from bilinear forms, where
alternating means (v,v)=0, antisymmetric means (v,w)=-(w,v) and symmetric
means (v,w)=(w,v). "alternating" is not "antisymmetric" in characteristic
2.
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Ticket URL: <http://trac.sagemath.org/ticket/15245#comment:7>
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