Suppose that the positive definite matrix A has the Cholesky factorization A = L Lt and

Chapter 1, Problem 6.6.32

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Suppose that the positive definite matrix A has the Cholesky factorization A = L Lt and also the factorization A = L D Lt , where D is the diagonal matrix with positive diagonal entries d11, d22, ... , dnn . Let D1/2 be the diagonal matrix with diagonal entries d11, d22, ... , dnn . a. Show that D = D1/2D1/2. b. Show that L = L D 1/2

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