The P -property of the following two Z-transformations with respect to the positive semidefinite cone is characterized: (i) I − S, where S : S → S is a nilpotent linear transformation, (ii) I − L A , where LA is the Lyapunov transformation defined on S n×n by LA(X) = AX + XA . (Here S denotes the space of all symmetric n×n matrices and I is the identity transformation.)

It is shown that every ray transfer matrix, often called the ABCD matrix, can be written as a similarity transformation of one of the Wigner matrices that dictate the internal space-time symmetries of relativistic particles, while the transformation matrix is a rotation preceded by a squeeze. The implementation of this mathematical procedure is described, and how it facilitates the calculations...

A transformation of polynomial matrices which preserves both the finite and infinite elementary divisor structure is presented and related to other known transformations.

The row by row decoupling problem (RRDP) for descriptor systems is considered using proportional state feedback and input transformation. Necessary and sufficient conditions for the solvability of the RRDP are provided. These solvability conditions can be readily verified. A constructive solution to the RRDP is given so that the desired feedback and input transformation matrices can be obtained...

In several domains of physics like, for instance, in string theory [1] and in quantum chromodynamics [2] we are interested in the spectral properties of random matrices; most results in this domain are included in the correlation functions for the invariants of the matrices like determinants, traces...Although most interesting results are expected from infinitely large matrices, exact results c...

We have shown previously that vocal tract normalization (VTN) results in a linear transformation in the cepstral domain. In this paper we show that Mel-frequency warping can equally well be integrated into the framework of VTN as linear transformation on the cepstrum. We show examples of transformation matrices to obtain VTN warped Mel-frequency cepstral coefficients (VTN-MFCC) as linear transf...

We consider here passive mechanical wrists, capable of imparting a desired dumping matrix to a grasped workpiece. Previous work 112. 131 has shown how to select a dumping matrix such that an assembly operatwn can be modc force-guided Thc passive mechanical wrist is to be progmnvnable it can adopt a widc range of damping matrices by virtue of a number of t u d e dampers which inrcrconneet the jo...

The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasise...