Decompositions of Pseudo-Unitary and Centro-Unitary Matrices

Abstract

ConsiderCn as the pseudo-unitary space with the inner product defined by the matrix\( {p}_n=\left(\begin{array}{l}\kern4em 1\hfill \\ {}\kern3em 1\hfill \\ {}\kern1em \dots \hfill \\ {}1\hfill \end{array}\right) \).

In this space, centro-unitary matrices play the role of unitary operators.

The main result of this paper is a factorization of an arbitrary centro-unitary matrix of even order into a product of simpler centro-unitary matrices. This result is an implication of a similar fact concerning factorizations of pseudo-unitary matrices of the type (n, n).