Exercise 6.5.13

Answers

The necessity is false. For example, the two matrices $(\begin{matrix} 1 & - 1 \\ 0 & 0 \end{matrix})$ and

(\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}) = {(\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix})}^{- 1} (\begin{matrix} 1 & - 1 \\ 0 & 0 \end{matrix}) (\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix})

are similar. But they are not unitary since one is symmetric but the other is not.

jephianlin

2011-06-27 00:00