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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. [ABSTRACT FROM AUTHOR]

A simple recursive scheme for parametrization of n-by-n unitary matrices is presented. The n-by-n matrix is expressed as a product containing the (n-1)-by-(n-1) matrix and a unitary matrix that contains the additional parameters needed to go from n-1 to n. The procedure is repeated to obtain recursion formulas for n-by-n unitary matrices. [ABSTRACT FROM AUTHOR]

Studies a general method to map a polynomial recursion on a matrix linear one. Product of a matrix multiplied by the vector of initial values; Transfer matrices.