Schlesinger transformations are discrete monodromy preserving symmetry transformations of a meromorphic connection which shift by integers the eigenvalues of its residues. We study Schlesinger transformations for twisted slN -valued connections on the torus. A universal construction is presented which gives the elementary two-point transformations in terms of Belavin’s elliptic quantum R-matrix...

Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, D 04109 Leipzig, Germany Abstract In this paper, three methods for describing the conformal transformations of the S-matrix in quantum field theory are proposed. They are illustrated by applying the algebraic renormalization procedure to the quantum scalar field theory, defined by the LSZ reduction mechanism in the BPHZ...

In mathematics, complete classification of structures, such as groups and rings, is often a primary goal. Linear transformations are no exception to this. Certain canonical forms exist to classify linear transformations, therefore creating a unique representative of linear transformations in the same similarity class. Diagonal representation is of course one of the simplest examples of a canoni...

in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i & ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i & ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

In this paper, we propose the use of complex-orthogonal transformations for nding the eigenvalues of a complex symmetric matrix. Using these special transformations can signiicantly reduce computational costs because the tridiagonal structure of a complex symmetric matrix is maintained.

8 Matrices 16 8.1 Representation of vector spaces and linear transformations . . . . . . . . . . . . . . . 16 8.2 Similarity transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 8.3 Direct sums of matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 8.4 The companion matrix of a polynomial . . . . . . . . . . . . . . . . . . . . . . . ....

In this paper we describe uniied formulas for unitary and hyperbolic reeections and rotations, and show how these uniied transformations can be used to compute a Hermitian triangular decomposition ^ R H D ^ R of a strongly nonsingular indeenite matrix ^ A given in the form ^ The uniication is achieved by the introduction of signature matrices which determine whether the applicable transformatio...

2D graphics transformations are represented as matrices. J programs for manipulating transformations such as scaling, rotation and translation are given. Efficiency of matrix representation of transformations is discussed. Subject Areas: 2D Graphics Transformations.

We prove general results that reduce the determination of the β–duals of matrix domains XT of triangles in certain FK spaces X to that of the β–dual of X, and the characterization of matrix transformations on XT to that of matrix transformations on X. AMS Mathematics Subject Classification (2000): 40H05, 46A45