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'skew-symmetric bilinear form'
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| Title of object: |
skew-symmetric bilinear form |
| Canonical Name: |
SkewSymmetricBilinearForm |
| Type: |
Definition |
| Created on: |
2002-11-28 07:33:27 |
| Modified on: |
2002-11-28 07:33:27 |
| Classification: |
msc:15A63 |
| Defines: |
skew symmetric, anti-symmetric, antisymmetric |
| Synonyms: |
skew-symmetric bilinear form=antisymmetric bilinear form
skew-symmetric bilinear form=anti-symmetric bilinear form |
Revision comment (for changes between this and next version):
| Expand and clarify entry. Add a more formal definition. |
Preamble:
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Content:
A {\em skew-symmetric} (or {\em antisymmetric}) {\em bilinear form} is a bilinear form $B$ which is skew-symmetric in the two coordinates; that is, $B(x,y) = -B(y,x)$ for all vectors $x$ and $y$. In particular, this means that $B(x,x)=0$.
A bilinear form is skew-symmetric iff its defining matrix is skew-symmetric. |
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