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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2014 • Question 1

Question

Math 6610 • Analysis of Numerical Methods I Fall 2014 • Question 1

Let \(A\) be an \(m\times n\) matrix where you may assume that \(m\geq n\). Define what is meant by the Singular Value Decomposition of \(A\). Then use it to show that if the rank of \(A\) is \(p\) then there exists an \(m\times p\) matrix \(X\) and an \(n\times p\) matrix \(Y\) such that \[ A=XY^T. \]

Raw LaTeX

Let \(A\) be an \(m\times n\) matrix where you may assume that
\(m\geq n\). Define what is meant by the Singular Value Decomposition of \(A\). Then
use it to show that if the rank of \(A\) is \(p\) then there exists an \(m\times p\)
matrix \(X\) and an \(n\times p\) matrix \(Y\) such that
\[
  A=XY^T.
\]

Topic Tags

Linear Programming and Optimization Singular Value Decomposition