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Exercise 6.10.3

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If $B$ is real symmetric, then we have $B^{∗} B = B^{2}$ . If $λ$ is the largest eigenvalue of $B$ , then we have $λ^{2}$ is also the largest eigenvalue of $B^{2}$ . Apply the Corollary 1 after Theorem 6.43 and get that $∥ B ∥ = λ$ . If $B$ is not real, the eigenvalue of $B$ may not be a real number. So they are not comparable. Hence we need the condition that $B$ is a real matrix here.

jephianlin

2011-06-27 00:00

Exercise 6.10.3

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