Abstract: Let B ∈ Cn×n denote a finite-dimensional square complex matrix. In [6] and [7], Professor Varga and I introduced Geršgorin-type sets which were developed from Singular Value Decompositions (SVDs) of B. In this note, our work is extended by introducing the polar SV-Geršgorin set, Γ(B). The set Γ(B) is a union of n closed discs in C, whose centers and radii are defined in terms of the e...

Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution σ of G. We prove a polar decomposition G = KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of groups Ai which are the k-points of maximal (k, σ)-split tori, one for each H-conjugacy class. T...

This paper presents an analysis of the channel capacity for 2×2 multiple input multiple output (MIMO) antenna systems. In this research, channel capacity is simultaneously analyzed by arbitrary transmitting (Tx) and receiving (Rx) antenna correlation matrix with correlated fading channel matrix. The channel capacity for 2×2 MIMO system is calculated. Considered parameters include receiving sign...

In [F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2 case, Linear Algebra Appl., 38:239–249, 1981], the author gives a representation for the factors of the polar decomposition of a nonsingular real square matrix of order 2. Uhlig’s formulae are generalized to encompass all nonzero complex matrices of order 2 as well as all order n complex matrices with ran...

A reenement of the polar decomposition of a nonsingular matrix A is considered. Here A is written as a product of unitary U ; Hermitian and positive deenite P which has unit diagonal, and diagonal positive D : It is shown that such a decomposion exists and is unique. Rectangular and singular cases are also considered. Then a simple xed point iteration using SVD is given to compute this decompos...

In this paper, polar and spherical Fourier Analysis are defined as the decomposition of a function in terms of eigenfunctions of the Laplacian with the eigenfunctions being separable in the corresponding coordinates. Each eigenfunction represents a basic pattern with the wavenumber indicating the scale. The proposed transforms provide an effective radial decomposition in addition to the well-kn...

Theobjective in this paper to study and present a new iterative method possessing high convergence order for calculating the polar decompostion of a matrix. To do this, it is shown that the new scheme is convergent and has high convergence. The analytical results are upheld via numerical simulations and comparisons.