16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.3.9

Bilinear Forms

Mathematics — Linear Algebra · skew-form-from-functionals

Problem

Let VV be a finite-dimensional vector space and L1L_1, L2L_2 linear functionals on VV. Show that the equation f(α,β)=L1(α)L2(β)−L1(β)L2(α)f(\alpha, \beta) = L_1(\alpha) L_2(\beta) - L_1(\beta) L_2(\alpha) defines a skew-symmetric bilinear form on VV. Show that f=0f = 0 if and only if L1L_1, L2L_2 are linearly dependent.

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