Exercise 5.6.4

Question

Show that a product of unitary (orthogonal) matrices is unitary (orthogonal) as well.

Jing Huang · Accepted Answer

\begin{proof}
Suppose $U_1, U_2$ are unitary (orthogonal), then $$(U_1U_2)^*U_1U_2 = U_2^*U_1^*U_1U_2 = U_2^* I U_2 = I.$$ From Lemma 6.2, we know the product is unitary (orthogonal).
\end{proof}

Exercise 5.6.4

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Exercise 5.6.4

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