Abstract: Besides different definitions, in this work is given the so called transformation matrix, which maps the given index space in another index space. Transformation used in this new index space reduces the number of processing elements in the array. We illustrate all possible instances of transformation matrices and we show the importance of using the transformation matrix by comparing t...

In this paper, the effect of normal impact on the mathematical modeling of flexible multiple links is investigated. The response of such a system can be fully determined by two distinct solution procedures. Highly nonlinear differential equations are exploited to model the falling phase of the system prior to normal impact; and algebraic equations are used to model the normal collision of this ...

Dixon 1908] introduces three distinct determinant formulations for the resultant of three bivariate polynomials of bidegree (m; n). The rst technique applies Sylvester's dialytic method to construct the resultant as the determinant of a matrix of order 6mn. The second approach uses Cayley's determinant device to form a more compact representation for the resultant as the determinant of a matrix...

This paper describes a principled application of twodimensional principal component analysis (2DPCA) to the decomposition of transformation matrices of maximum likelihood linear regression (MLLR) and its application to speaker adaptation using the bases derived from the analysis. Our previous work applied 2DPCA to speaker-dependent (SD) models to obtain the bases for state space. In this work, ...

Dirac matrices, also known as gamma matrices, are defined only up to a similarity transformation. Usually, some explicit representation of these matrices is assumed in order to deal with them. In this article, we show how it is possible to proceed without any such assumption. Various important identities involving Dirac matrices and spinors have been derived without assuming any representation ...