Explain why the singular values of A are the same as the nonzero eigenvalues of the positive
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Explain why the singular values of A are the same as the nonzero eigenvalues of the positive definite square root matrix S = √ATA , defined in Exercise 8.5.27.
Data From Exercise 8.5.27
(a) Prove that every positive definite matrix K has a unique positive definite square root, i.e., a matrix B > 0 satisfying B2 = K.(b) Find the positive definite square roots of the following matrices:
(i)
(ii)
(iii)
(iv)
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