16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.2.6

Bilinear Forms

Mathematics — Linear Algebra · diagonalizing-quadratic-form

Problem

Let qq be the quadratic form on R2R^2 given by q(x1,x2)=2bx1x2.q(x_1, x_2) = 2bx_1 x_2. Find an invertible linear operator UU on R2R^2 such that (U†q)(x1,x2)=2bx12−2bx22.(U^\dagger q)(x_1, x_2) = 2bx_1^2 - 2bx_2^2.

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