Events
DMS Linear Algebra/Algebra Seminar |
Time: Oct 09, 2018 (04:00 PM) |
Location: Parker Hall 354 |
Details: Speaker: Tin-Yau Tam Title: The relation of a nonsingular matrix and its components in polar decomposition Abstract: Each nonsingular matrix A has the so called polar decomposition A = PU (or UP) where P is positive definite and U is unitary. The Weyl--Horn Theorem gives a nice relation between the eigenvalues of A and the eigenvalues of P. The relation is known as log majorization and is on the moduli of the eigenvalues of A and P. Kostant extended the result in the context of semisimple Lie groups. The Horn--Steinberg Theorem gives a nice relation between the eigenvalues of A and the eigenvalues of U. The relation is on the arguments of the eigenvalues A and the arguments of the eigenvalues of U. We will review these two theorems and provide some progress toward the extension of Horn--Steinberg Theorem in the context of complex semsimple Lie groups. |