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Let the eigenvalues of a matrix of order 3 be 1,2, - 2, and B = 3a2-a3, then find the diagonal matrix with eigenvalues similar to B | B | a-3i |? (the number after a is superscript)
The general result is that if the eigenvalues of a are A1, A2,..., an, then for any polynomial f (x), the eigenvalues of B = f (a) are f (A1), f (A2),..., f (an). Now f (x) = 3x ^ 2-x ^ 3, so the eigenvalues of B are 3 (1 ^ 2) - 1 ^ 3,3 (2 ^ 2) - 2 ^ 3,3 ((- 2) ^ 2) - (- 2) ^ 3, that is, the eigenvalues of 2,4,20 are different, so B
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