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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2024 • Question 4

Question

Math 6610 • Analysis of Numerical Methods I Fall 2024 • Question 4

(Properties of the SPD Matrices) Let \(A \in \mathbb {R}^{n \times n}\) be a symmetric positive definite matrix (spd). Show that there exists a unique upper triangular matrix \(H \in \mathbb {R}^{n \times n}\) with positive diagonal entries such that, \(A = H^T H\).

Raw LaTeX

(Properties of the SPD Matrices)
Let \(A \in \mathbb{R}^{n \times n}\) be a symmetric positive definite matrix (spd). Show that there exists a unique
upper triangular matrix \(H \in \mathbb{R}^{n \times n}\) with positive diagonal entries such that, \(A = H^T H\).

Topic Tags

Cholesky Factorization and SPD Matrices Linear Programming and Optimization