16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8

Inner Product Spaces

Mathematics — Linear Algebra · unitary-equivalence

Problem

If θ\theta is a real number, prove that the following matrices are unitarily equivalent [cos⁡θ−sin⁡θsin⁡θcos⁡θ],[eiθ00e−iθ]\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}, \quad \begin{bmatrix} e^{i\theta} & 0 \\ 0 & e^{-i\theta} \end{bmatrix}

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