Exercise 6.5.24

Answers

1.

First, the composition of two unitary operators is again an unitary operator. So

UT

is an unitary operator. Since

\det (U) = \det (T) = - 1

, we have

\det (UT) = \det (U) \det (T) = 1 .

This means that $UT$ must be a rotation by Theorem 6.23.

2.

It’s similar to the previous argumemnt. And now we have

\det (UT) = \det (TU) = \det (T) \det (U) = 1 \cdot (- 1) = - 1 .

So they are reflections.

jephianlin

2011-06-27 00:00