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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2012 • Question 1

Question

Math 6610 • Analysis of Numerical Methods I Spring 2012 • Question 1

Full rank matrix

Given \(A\in \mathbb {C}^{m\times n}\) with \(m\geq n\), show that \(A^*A\) is nonsingular if and only if \(A\) has full rank.

Raw LaTeX

{Full rank matrix}

Given \(A\in\C^{m\times n}\) with \(m\geq n\), show that \(A^*A\) is nonsingular if
and only if \(A\) has full rank.

\vspace{1.2\baselineskip}

Topic Tags

Linear Programming and Optimization Matrix Rank and Fundamental Linear Algebra