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
Recommended Citation
Bhattacharjee, Monika and Bose, Arup, "Matrix polynomial generalizations of the sample variance-covariance matrix when pn −1 → y ∈ (0, ∞)" (2017). Journal Articles. 2308.
https://digitalcommons.isical.ac.in/journal-articles/2308