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Exercise 6.7.13

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If $A$ is a positive semidefinite matrix with eigenvalues $λ_{i}$ ’s, we know that $A^{∗} = A$ and so $λ_{i}$ is real and nonnegative. Furthermoer, we have

A^{∗} A (x) = A^{2} (x) = λ_{i}^{2} x .

Since $λ_{i} \geq 0$ , we have $\sqrt{λ_{i}^{2}} = λ_{i}$ . Hence the eigenvalues of $A$ are the singular values of $A$ .

jephianlin

2011-06-27 00:00

Exercise 6.7.13

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