Fraikin, Catherine (Univ. catholique de Louvain), Nesterov, Yurii (Catholic Univ. of Louvain (UCL)), Van Dooren, Paul Michel (Univ. Catholique de Louvain)

Coupling between Orthogonally Projected Matrices

Scheduled for presentation during the Mini-Symposium "Geometric Optimisation in Systems and Control I" (WeA07), Wednesday, July 26, 2006, 10:25−10:50, Room H

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 26, 2024

Abstract

We consider the problem of finding the optimal coupling between two restricted matrices $U^*AU$ and $V^*BV$ under isometry constraints $U^*U=V^*V=I_k$. The square matrices $A$ and $B$ may be of different dimensions, but the isometries $U$ and $V$ have a common column dimension $k$. The coupling is measured by the real function $Re tr(U^*AUV^*B^*V)$, which we maximize over $U$ and $V$.

This problem can be viewed as an extension of the generalized numerical range of two matrices, which are now allowed to be of different dimension. We discuss several properties of this optimization problem, characterize its extremal points and propose an algorithm converging to such an extremal point.