Title: Morphisms of complex Hadamard matrices
|Speaker:||Padraig O Cathain|
|Affiliation:||Worcester Polytechnic University|
Let M be a matrix with complex entries of unit norm. A well-known theorem of Hadamard bounds the magnitude of the determinant of M as a function of its dimension, and M is a complex Hadamard matrix if M meets Hadamard's bound with equality. In this talk we will survey some known results on existence of special types of complex Hadamard matrices, in particular matrices with entries in the k-th roots of unity. I will report on recent joint work with Ronan Egan on the existence of tensor-product-like maps which reduce the number of entries in a complex Hadamard matrix at the cost of increasing the dimension. This work generalises previous constructions of Turyn and Compton-Craigen-de Launey of real Hadamard matrices from certain complex Hadamard matrices. No previous knowledge of Hadamard matrices will be assumed.
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