Question: 20. Let h(x) = n i=0 a i x i be a polynomial. Define h(A) by h(A)= n i=0 a i A i

20. Let h(x) = Σni=0 aixi be a polynomial. Define h(A) by h(A)= Σni=0 aiAi.

where A0 = I and ai are scalars. If λ1, λ2, ..., λn are the characteristic roots of the n x n matrix A, show that tr [h(A)] = Σni=1 h(λi).

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