Open AccessOn some Toeplitz matrices and their inversions
Author(s) -
S. Dutta,
P. Baliarsingh
Publication year - 2014
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.10.001
Subject(s) - toeplitz matrix , mathematics , combinatorics , inverse , triangular matrix , matrix (chemical analysis) , operator (biology) , invertible matrix , pure mathematics , geometry , biochemistry , chemistry , materials science , composite material , repressor , transcription factor , gene
In this article, using the difference operator B(a[m]), we introduce a lower triangular Toeplitz matrix T which includes several difference matrices such as Δ(1),Δ(m),B(r,s),B(r,s,t), and B(r̃,s̃,t̃,ũ) in different special cases. For any x ∈ w and m∈N0={0,1,2,…}, the difference operator B(a[m]) is defined by (B(a[m])x)k=ak(0)xk+ak-1(1)xk-1+ak-2(2)xk-2+⋯+ak-m(m)xk-m,(k∈N0) where a[m] = {a(0), a(1), …, a(m)} and a(i) = (ak(i)) for 0 ⩽ i ⩽ m are convergent sequences of real numbers. We use the convention that any term with negative subscript is equal to zero. The main results of this article relate to the determination and applications of the inverse of the Toeplitz matrix T