Urgent plzz..hand written 3.27 Diagonal elements of Cholesky factor. Each X E S has a unique Cholesky factorizationX = LLT, where L is lower triangular, with Lü > 0. Show that Lii is a concave functionof X (with domain S).Hint. Lii can be expressed as Lii = (w – zTY-12)/2, whereYTwis the leading i xi submatrix of X.

Given That : Each X∈Sn++ has a unique Cholesky factorization X=LLT where L is a lower triangular…

Answered: Diagonal elements of Cholesky factor.…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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Diagonal elements of Cholesky factor. Each X ES+ has a unique Cholesky factorization X = LLT, where L is lower triangular, with Li> 0. Show that Lii is a concave function of X (with domain S2+). Hint. Lii can be expressed as Lii = (w - zTY-12) ¹/2, where is the leading ix i submatrix of X. Y T 2 W