The combinatorial power of the companion matrix
type: Item
instance of: scholarly article
title: The combinatorial power of the companion matrix
zbMATH Open document ID: 0838.15015
DOI: 10.1016/0024-3795(95)90163-9
author: William Y. C. Chen
author: J. D. Louck
published in: Linear Algebra and its Applications
publication date: 1996-02-06T00:00:00Z
review text: The explicit polynomials for all elements in an arbitrary power of the companion matrix depending on \(n\) variables are obtained using combinatorial methods. Several applications are discussed as well as the relationship with Waring's formula on symmetric functions, the general solution to homogeneous linear recurrence relations, the multiplicative inverse of formal power series, the generating function of compositions (of numbers), a unified approach to Chebyshev polynomials, Dickson polynomials of various kinds arising from the theory of finite fields and combinatorial expansions of Toeplitz matrices.
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 841764
zbMATH Keywords: combinatorial power
zbMATH Keywords: companion matrix
zbMATH Keywords: Waring's formula
zbMATH Keywords: recurrence relations
zbMATH Keywords: formal power series
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Dickson polynomials
zbMATH Keywords: finite fields
zbMATH Keywords: Toeplitz matrices
reviewed by: Giacomo Bonanno
MaRDI profile type: Publication
full work available at URL: 0024-3795(95)90163-9
OpenAlex ID: W1985900997
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description: scientific article; zbMATH DE number 841764