Ex5 1

$\def\abs#1{|#1}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 5.1}$

Show that any linear transformation $U$ that takes unit vectors to unit vectors preserves orthogonality: if subspaces $S_1$ and $S_2$ are orthogonal, then so are $U S_1$ and $U S_2$.

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