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Let $M$ be a complex matrix $$M:=\begin{bmatrix} 0 & i & -i \\ i & 0 & 1 \\ -i & 1 & 0 \\ \end{bmatrix}$$ 1) Find a unitary complex matrix $Q$ such that $Q^HMQ$ is an upper-triangular matrix.

2) Find a unitary complex matrix $P$ such that $(MP)^H(MP)$ is a diagonal matrix.

I'm just starting in to a self-study of sorts with complex linear algebra and ran across this type of problem. I'm not even sure how to attack this and any advice would be great!

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  • $\begingroup$ You can see an example for the real case for 1) here. $\endgroup$ – Git Gud May 7 '16 at 20:17

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