Suppose I have a nondegenerate alternating bilinear form <,> on a vector space V. Under what conditions would a subspace U of V retain nondegeneracy? That is, if u ∈ U and u ≠ 0, then could I find a w ∈ U such that <u,w> ≠ 0?(adsbygoogle = window.adsbygoogle || []).push({});

So for example, it's clear that no one-dimensional subspace W of V could retain nondegeneracy since every vector in W could be written as a scalar multiple of any other. But would, say, a two-dimensional subspace retain nondegeneracy?

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# Which subspaces retain nondegeneracy of a bilinear form?

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