In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with q a root of unity. Since the q-deformed boson algebra was known [1,2], much work has been accomplished in this direction [3-8]. It is well known that this algebra has an infinite dimensional representation when the deformation parameter q is real, while it has a finite ...

We show how one may obtain polar decomposition as well as inversion of xed and time-varying matrices using a class of nonlinear continuous-time dynamical systems. First we construct a dynamic system that causes an initial approximation of the inverse of a time-varying matrix to ow exponentially toward the true time-varying inverse. Using a time-parameterized homotopy from the identity matrix to...