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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2012 • Question 2

Question

Math 6610 • Analysis of Numerical Methods I Spring 2012 • Question 2

\(QR\) and Cholesky Factorizations

Let \(A\) be a nonsingular square matrix and let \(A=QR\) and \(A^*A=U^*U\) be the \(QR\) factorization of \(A\) and the Cholesky factorization of \(A^*A\), respectively. Assume that the usual normalizations \(r_{jj},u_{jj}>0\) are in effect. Is it true or false that \(R=U\)? Justify your answer.

Raw LaTeX

{\(QR\) and Cholesky Factorizations}

Let \(A\) be a nonsingular square matrix and let \(A=QR\) and \(A^*A=U^*U\) be the
\(QR\) factorization of \(A\) and the Cholesky factorization of \(A^*A\),
respectively. Assume that the usual normalizations \(r_{jj},u_{jj}>0\) are in
effect. Is it true or false that \(R=U\)? Justify your answer.

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Topic Tags

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