Kunze Linear Algebra · Problem 10.1.11

Bilinear Forms

Mathematics — Methods · rank-lower-bound-bilinear-form

Problem

Let

f

be a bilinear form on a finite-dimensional vector space

V

. Suppose

V_1

is a subspace of

V

with the property that the restriction of

f

V_1

is non-degenerate. Show that

\text{rank}\, f \geq \dim V_1