## Nielsen and Chuang Exercise 2.16

Exercise 2.16Show that any projector satisfies .

Any projector may be written

Thus,

## Nielsen and Chuang Exercise 2.15

Exercise 2.15Show that

(Getting a little lazy with the equation typesetting here…) The adjoint is a combination of two operations, the transpose, and the complex conjugate, both of which are identity when applied twice. Thus, the combination of them applied twice also yields the identity operation.

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