Kunze Linear Algebra · Problem 10.1.14

Bilinear Forms

Mathematics — Methods · rank-one-bilinear-form

Problem

Let ff be a bilinear form on a finite-dimensional vector space VV. Show that ff can be expressed as a product of two linear functionals (i.e., f(α,β)=L1(α)L2(β)f(\alpha, \beta) = L_1(\alpha)L_2(\beta) for L1,L2L_1, L_2 in V∗V^*) if and only if ff has rank 11.

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