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 propose a differential evolution (DE) algorithm which aims to optimize a system whose parameters form a multidimensional array. Determination of the optimal demixing matrix in a blind signal separation problem can be considered as an example of this type of system. Since the DE algorithm performs only on column vectors, it can be used after the multidimensional array is transf...

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...

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

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

This paper presents a novel vector quantization (VQ) technique in which the quantized vector is formed by adding the transformed outputs of a multistage codebook rather than just adding the outputs of the stages as in regular multistage vector quantization (MSVQ). The transformations are selected from a family of linear transformations represented by a codebook of matrices. This technique can b...