Math 6610 • Analysis of Numerical Methods I

{Singular Value Decomposition}
Define the singular value decomposition of a real \(m\times n\) matrix with \(m\ge n\).
Is the SVD unique for a given matrix \(A\)? How is an SVD problem connected with an
eigendecomposition of a symmetric matrix? Sketch the general structure of algorithms
for those imported from eigendecomposition, namely, how do you reduce \(A\) to some
form more manageable? How do you obtain the information about the rank of \(A\)
through the SVD of \(A\)? If \(A\) is square and nonsingular, how does the SVD of \(A\)
help you determine the sensitivity of the solution \(x\) for \(Ax=b\)?