Recursive parametrization and invariant phases of unitary matrices

Abstract

We present further properties of a previously proposed recursive scheme for parametrization of n -by- n unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study the invariant phases of unitary matrices. The case of four-by-four unitary matrices is investigated in detail. We also address the question of how to construct symmetric unitary matrices (i.e., unitary matrices U that satisfy the condition Uij = Uji) using the recursive approach. © 2006 American Institute of Physics.