Research Seminar in Mathematics - Generalizing Orthogonal Matrices: On the Structure of the Solutions to the Matrix Equation G*JG=J
04 March 2022 13:15 Zoom
Please contact Andrii Dmytryshyn if you have any questions regarding this seminar series.
Speaker
Alan Edelman, Massachusetts Institute of Technology .
Join Zoom meeting
Meeting ID: 694 4974 3647 Passcode: 389449
Abstract
We study the mathematical structure of the solution set to the matrix equation G*JG=J for a given square matrix J. In the language of pure mathematics, this is a Lie group which is the isometry group for a bilinear (or a sesquilinear) form.
We found that on its own, the related (tangent space) equation X*J+JX= 0 is hard to solve. By throwing into the mix the complementary linear equation X*J−JX= 0, we find that rather than increasing the complexity, we reduce the complexity.
We explicitly demonstrate computation of solutions, visualizations, and closure hierarchies that connect to previous work by Dmytryshyn, Futorny, Kågström, Klimenko, and Sergeichuk.
Joint work with Sung Woo Jeong.
Welcome!