What is the smallest possible dimension for a vector space with a non-degenerate skew-symmetric bilinear form? Why?
I really don't know how to approach this problem.
2026-03-29 06:36:38.1774766198
What is the smallest possible dimension for a vector space with a non-degenerate skew-symmetric bilinear form? Why?
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You can easily construct an example.
Try the bilinear form that takes $(a,b)$ and $(c,d)$ to $ad-bc$.