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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2018 • Question 1

Question

Math 6610 • Analysis of Numerical Methods I Spring 2018 • Question 1

Projections

Let \(P\in \mathbb {C}^{N\times N}\) be a projection matrix. Prove that \(\ker (P)\perp \operatorname {range}(P)\) if and only if \(P=P^*\). (I.e., you are being asked to justify the definition of an orthogonal projection matrix.)

Raw LaTeX

{Projections}

Let \(P\in\C^{N\times N}\) be a projection matrix. Prove that
\(\ker(P)\perp\operatorname{range}(P)\) if and only if \(P=P^*\). (I.e., you are
being asked to justify the definition of an orthogonal projection matrix.)

Topic Tags

Linear Programming and Optimization Orthogonal and Unitary Matrices Projectors and Orthogonal Projections