16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 9.3.2

Operators on Inner Product Spaces

Mathematics — Linear Algebra · positive-operators-rotation

Problem

Let VV be R2R^2, with the standard inner product. If θ\theta is a real number, let TT be the linear operator 'rotation through θ\theta,' Tθ(x1,x2)=(x1cos⁡θ−x2sin⁡θ, x1sin⁡θ+x2cos⁡θ).T_\theta(x_1, x_2) = (x_1 \cos\theta - x_2 \sin\theta,\ x_1 \sin\theta + x_2 \cos\theta). For which values of θ\theta is TθT_\theta a positive operator?

Related theory

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