PhD Math Defence: Complex Matrix Scalings, Extremal Permanents, and the Geometric Measure of Entanglement
CANDIDATE: GEORGE HUTCHINSON
ABSTRACT:
An n x n matrix with complex entries is said to be doubly quasi-stochastic (DQS) if all row and column sums are equal to one. Given a positive definite matrix A and a diagonal matrix D, we say that D*AD is a (complex matrix) scaling of A if D*AD is doubly quasi-stochastic. Motivated by a result of Pereira and Boneng concerning the application of complex matrix scalings to the geometric measure of entanglement of certain symmetric states, we embark upon an investigation of these scalings and their properties.