Events

COSAM Events 2015 September Graduate Student Seminar

Graduate Student Seminar

Time: Sep 16, 2015 (03:00 PM)
Location: Parker Hall 249

Details:

Speaker: Mr. Daryl Granario

Title: Matrix polar decompositions and canonical forms
 
The classical polar decomposition of a complex square matrix is its factorization into a product of a unitary matrix and a positive semidefinite Hermitian matrix. Two other analogous polar decompositions are well-known: the algebraic polar decomposition (orthogonal-symmetric) and the circular polar decomposition (real-coninvolutory). In this talk, we look at general polar decompositions induced by antihomomorphic spectrum preserving linear maps. We use canonical forms and other results in matrix analysis to provide necessary and sufficient conditions for the existence of these polar decompositions.