Infinite Vector Decomposition in Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) Perspective

Abstract

In this work a new version of Enhanced Multivariance Products Representation (EMPR) is taken into consideration. Recent researches on the bivariate arrays (i.e., Matrices) have led us to a new scheme which we have called Tridiagonal Matrix Enhanced Multivariate Products Representation (TMEMPR). Therein we have been consecutively using four term EMPR on its bivariate component under different support functions such that the remainder was becoming to have less rank as we proceed until no bivariate component remains. Here however, we focus on denumerably infinite vectors and first appropriately fold them to semi infinite matrices with finite number of denumerable infinite rows, then decompose the resulting infinite matrices via TMEMPR, and at the final stage we unfold each additive term of the representation via unique inversion of the folding procedure we use.