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Exercise 6.5.4

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Pick the standard basis $β$ and compute the matrix representation ${[T_{x}]}_{β} = (\begin{matrix} z \end{matrix})$ . This means that $T_{z}^{∗} = T_{\bar{z}}$ . So it always would be normal. However, it would be self-adjoint only when $z$ is real. And it would be unitary only when $| z | = 1$ .

jephianlin

2011-06-27 00:00

Exercise 6.5.4

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