Minimal polynomials of complex Hadamard matrices
Complex Hadamard matrices have entries of unit norm and rows orthogonal under the Hermitian inner product. Such matrices meet Hadamard's determinant bound with equality.
In this talk I will discuss results obtained jointly with Ronan Egan and Eric Swartz on generalised tensor product constructions for Hadamard matrices in which conditions on the minimal polynomial of one of the matrices arise. Special cases of this construction capture results of Turyn, Compton-Craigen-de Launey, Mukhopadhyay-Seberry and Ostergaard-Paavola. Time permitting, I will discuss techniques for controlling the minimal polynomial of a Hadamard matrix, and connections to Mutually Unbiased Bases.
Padraig Ó Catháin, Worcester Polytechnic Institute