1. The problem statement, all variables and given/known data Let |v> ∈ ℂ^2 and |w> = A|v> where A is an nxn unitary matrix. Show that <v|v> = <w|w>. 2. Relevant equations * = complex conjugate † = hermitian conjugate 3. The attempt at a solution Start: <v|v> = <w|w> Use definition of w <v|v>=<A|v>A|v>> Here's the interesting part Using properties of a complex inner product, we can take out the unitary matrix A on the right hand side. When we do so, what do we get? Is it A*A or is it A†A ? If it is A†A this proof is complete, as sine A is unitary, this means A†A = the identity matrix and we get equality. If the definition is A*A then we have to do more work. I am getting mixed up, as I'm seeing both definitions floating around and with the abusive notation everywhere it is making me second guess which definition is right. Is there any clarity on this issue here?