We discuss the dynamical quantum systems which turn out to be biunitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the Hermitian structures are in generic position. Finally the transformations of the bi-unitary group are explicitly obtained.

A block Toeplitz algorithm is proposed to perform the J-spectral factorization of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The key assumption is that the finite zeros of the input polynomial matrix are given as input data. The algorithm is based on numerically reliable operations only, namely computation ...

In this paper we derive formulas for constructing the analytic center of the linear matrix inequality deening a positive (para-hermitian) transfer function. The Riccati equations that are usually associated with such positive transfer functions, are related to boundary points of the convex set. In this paper we show that the analytic center is also described by a closely related equation, and w...

This paper characterizes a class of regular para-Hermitian transfer matrices and then reveals the elementary characteristics of J -spectral factorization for this class. A transfer matrix in this class admits a J -spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of and −1, resp., into 2 × 2 lower (upper, resp.) triangular block...