I'm teaching myself quantum information theory using Nielson and Chuang's "Quantum Computation and Quantum Information" and I'm at a point in the book where the formalism is starting to make my eyes bleed.
Exercise 2.56 Use the spectral decomposition to show that $K \equiv -i\log(U)$ is Hermitian for an unitary $U$, and thus $U=\exp(iK)$ for some Hermitian $K$.
Using the defition of Hermitian e.g. $[A^\dagger]^\dagger=A$, I plugged the product $-i\log(U)$ and am now stuck. The problem for me is that I've been using these definitions in the context of matrix computations, but now the book is no longer connecting the operators to matrices as explicitly, expecting me to find the connections for myself.