Dimension of Orthogonal Complement With Respect to Bilinear Form
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Theorem
Let $\mathbb K$ be a field.
Let $V$ be a vector space over $\mathbb K$ of finite dimension.
Let $f$ be a nondegenerate bilinear form on $V$.
Let $U\subset V$ be a subspace.
Let $U^\perp$ be its orthogonal complement.
Then:
- $\map \dim U + \map \dim U^\perp = \map \dim V$
Proof
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