Given that the eigenvalues of the matrix are 5, 3 and 1: (a) Confirm Properties 14 of

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Given that the eigenvalues of the matrix

4 1 A = 25 54 |-1 -1 0

are 5, 3 and 1:

(a) Confirm Properties 1–4 of Section 5.7.6;

(b) Taking k = 2, confirm Properties 5–8 of Section 5.7.6.

Data from Section 5.7.6.

Property 1 The sum of the eigenvalues of A is   = trace A =   i=1 i=1 Property 2 The product of the

Property 4 The eigenvalues of the transposed matrix A are A, A2, An as for the matrix A. ..... Property 5 If

Property 7 If k is a positive integer then the eigenvalues of A* are dt, d ... dt Property 8 As a consequence

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