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Exercise 6.5.12

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By Theorem 6.19 and Theorem 6.20 we know that $A$ may be diagonalized as $P^{∗} AP = D$ . Here $D$ is a diagonal matrix whose diagonal entries consist of all eigenvalues. Now we have

\det (A) = \det (PD P^{∗}) = \det (D) = \prod_{i = 1}^{n} λ_{i} .

jephianlin

2011-06-27 00:00

Exercise 6.5.12

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