Description

Martin Jaggi & Ru¨diger Urbanke mlo.epfl.ch/page-157255-en-html/ epfmlcourse@gmail.com
Goals. The goal of this exercise is to
• familiarize yourself with the theory related to SVD.
• have time to discuss Project 2 with the assistants and teammates.
1 Theory Questions
Problem 1 (How to compute U and S efficiently):
In class, we saw that solving the eigenvector/value problem for the matrix XX> gives us a way to compute U and S. But in some instances . In those cases, is there a way to accomplish this computation more efficiently?
Problem 2 (Positive semi-definite):
Show that if X is a N×N symmetric matrix then the SVD has the form USU>, where U is a N×N unitary matrix and S is a N ×N diagonal matrix with non-necessarily positive entries. Show that if X is positive semi-definite, then all entries of S are non-negative.