Products of Unitary and Diagonal Matrices - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T01:20:28Z http://mathoverflow.net/feeds/question/38915 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/38915/products-of-unitary-and-diagonal-matrices Products of Unitary and Diagonal Matrices gappy3000 2010-09-16T02:22:34Z 2010-09-16T23:43:04Z <p>Every applied mathematician knows and uses the Singular Value Decomposition of a matrix, i.e., of products \$U^T D V\$, where \$D\$ is diagonal and \$U, V\$ are unitary. I am wondering if anything interesting can be said about products of the form \$D U E\$, in which \$D, E\$ are diagonal, and \$U\$ is unitary. What about their range and null space? And more generally what about the SVD of these matrices, in which we essentially swap the position of diagonal and unitary matrices? Any pointer to the literature is welcome. If \$D, E\$ are nonnegative and \$U \ne I\$, is it true that \$tr(DUE)>tr(DE)\$?</p>