Exercise 5.1.12

Answers

1.
Use the fact if A = P−1BP, then
det ⁡ (A − λI) = det ⁡ (P−1(A − λI)P)
= det ⁡ (P−1AP − λP−1IP) = det ⁡ (B − λI).
2.
Use the result of the previous exercise and the fact that each matrix representation of one linear operator is pairwisely similar to each other.
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2011-06-27 00:00
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