16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.1.11

Bilinear Forms

Mathematics — Linear Algebra · rank-non-degenerate-restriction

Problem

Let ff be a bilinear form on a finite-dimensional vector space VV. Suppose V1V_1 is a subspace of VV with the property that the restriction of ff to V1V_1 is non-degenerate. Show that rank f≥dim⁡V1\text{rank}\,f \geq \dim V_1.

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