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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2019 • Question 2

Question

Math 6610 • Analysis of Numerical Methods I Fall 2019 • Question 2

Matrix Factorizations

Let \(A\) be a nonsingular square real matrix and let \(A=QR\) and \(A^TA=H^TH\) be QR and Cholesky factorizations, respectively, with the usual normalizations \(r_{jj},h_{jj}>0\). Is it true or false that \(R=H\)? Justify your answer.

Raw LaTeX

{Matrix Factorizations}

Let \(A\) be a nonsingular square real matrix and let \(A=QR\) and
\(A^TA=H^TH\) be QR and Cholesky factorizations, respectively, with the usual
normalizations \(r_{jj},h_{jj}>0\). Is it true or false that \(R=H\)? Justify your
answer.

Topic Tags

Cholesky Factorization and SPD Matrices Linear Programming and Optimization Matrix Rank and Fundamental Linear Algebra QR Factorization