16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.1.1

Bilinear Forms

Mathematics — Linear Algebra · bilinear-forms-identification

Problem

Which of the following functions ff, defined on vectors α=(x1,x2)\alpha = (x_1, x_2) and β=(y1,y2)\beta = (y_1, y_2) in R2R^2, are bilinear forms? (a) f(α,β)=1f(\alpha, \beta) = 1. (b) f(α,β)=(x1−y1)2+x2y2f(\alpha, \beta) = (x_1 - y_1)^2 + x_2 y_2. (c) f(α,β)=(x1+y1)2−(x1−y1)2f(\alpha, \beta) = (x_1 + y_1)^2 - (x_1 - y_1)^2. (d) f(α,β)=x1y2−x2y1f(\alpha, \beta) = x_1 y_2 - x_2 y_1.

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