Algebraic Graph Theory Seminar - Chris Godsil

Thursday, January 25, 2018 1:30 pm - 1:30 pm EST (GMT -05:00)

Title: Type-II Matrices

Speaker Chris Godsil
Affiliation: University of Waterloo
Room MC 6486


The Schur product M o N of two matrices M and N is the usual entrywise product. The matrix N is the Schur inverse of M if M o N = J. Denote the Schur inverse of M by M(-). An n x n matrix is a type-II matrix if
WW(-)T = nI.
(Thus the usual inverse can be read from the Schur inverse.) Hadamard matrices provide one class of type-II matrices, but they occur in a surprising range of places.
I will discuss some of the basic properties of type-II matrices, and their connection with interesting objects such as symmetric designs and magic unitary matrices.