Title

Matrix polynomial generalizations of the sample variance-covariance matrix when pn −1 → y ∈ (0, ∞)

Article Type

Research Article

Publication Title

Indian Journal of Pure and Applied Mathematics

Abstract

Let {Zu = ((εu, i, j))p×n} be random matrices where {εu, i, j} are independently distributed. Suppose {Ai}, {Bi} are non-random matrices of order p × p and n × n respectively. Consider all p × p random matrix polynomials P=∏i=1kl(n−1AtiZjiBsiZji∗)Atkl+1. We show that under appropriate conditions on the above matrices, the elements of the non-commutative *-probability space Span {P} with state p−1ETr converge. As a by-product, we also show that the limiting spectral distribution of any self-adjoint polynomial in Span{P} exists almost surely.

First Page

575

Last Page

607

DOI

10.1007/s13226-017-0247-2

Publication Date

12-1-2017

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