This is one in a series of posts working through the exercises in the Quantum Country online introduction to quantum computing and related topics. The exercises in the original document are not numbered; I have added my own numbers for convenience in referring to them.
Exercise 9. Show that for any matrix and vector the following identity holds: .
Answer: By definition we have . It was shown in the text that . By definition we also have .
We then have
So we have shown that for any matrix and vector .