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Question: Normal Matrices

Question:Normal Matrices

dcasimir 1202
linear-algebra homework
October 30 2007
0
Again we have the unitary and Hermitian matrices U and H related by, U = exp(i*a*H) (a) If the trace of H = 0, show that the determinant of U = +1. (b) If the determinant of U = +1, show that the trace of H = 0. Given Hint: H may be diagonalized by a similarity transformation. Then interpreting the exponential by a Maclaurin expansion, U is also diagonal. The corresponding eigenvalues are given by u[j] = exp(i*a*h[j] v/r, Guidance welcomed and appreciated
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