Past exam of the mathematics course of the University of Cambridge / 2009 / ia / Paper 1 / 2B / Solution

For a complex matrix, its Hermitian conjugate is obtained by transposing and taking entrywise complex conjugates:The defining conditions areFor a square matrix, either one of the two inverse identities in the unitary matrix condition implies the other. A Hermitian matrix may have complex entries, but its diagonal entries are real.