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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2015 • Question 2

Question

Math 6610 • Analysis of Numerical Methods I Spring 2015 • Question 2

Positive Definite Matrices The Cholesky decomposition of a (symmetric and) positive definite matrix is defined to be a factorization of the form \(A=LL^T\) where \(L\) is lower triangular. Show that the Cholesky decomposition exists. Discuss whether or not it is unique.

Raw LaTeX

{Positive Definite Matrices} The Cholesky decomposition of a
(symmetric and) positive definite matrix is defined to be a factorization of the
form \(A=LL^T\) where \(L\) is lower triangular. Show that the Cholesky decomposition
exists. Discuss whether or not it is unique.

Topic Tags

Cholesky Factorization and SPD Matrices Linear Programming and Optimization QR Factorization Singular Value Decomposition