Integer Powers of Certain Complex (2k+1)-diagonal Toeplitz Matrices
H. K\"ubra Duru, Durmu\c{s} Bozkurt
TL;DR
This paper derives a general formula for the entries of integer powers of specific odd-order Toeplitz matrices and explores complex factorizations of Fibonacci polynomials, advancing understanding of their algebraic properties.
Contribution
It provides a novel explicit expression for powers of (2k+1)-diagonal Toeplitz matrices and introduces complex factorizations of Fibonacci polynomials.
Findings
Explicit formulas for matrix powers
Complex factorizations of Fibonacci polynomials
Enhanced understanding of Toeplitz matrix algebra
Abstract
In this paper, we obtain a general expression for the entries of the lth (l is integer) powers of even order (2k+1)-diagonal Toeplitz matrices. Additionally, we have the complex factorizations of Fibonacci polynomials.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · graph theory and CDMA systems · Graph Labeling and Dimension Problems