Generalized hyperbolic functions, circulant matrices and functional equations

The inverse matrix of some circulant matrices

We present here necessary and sufficient conditions for the invertibility of circulant and symmetric matrices that depend on three parameters and moreover, we explicitly compute the inverse. The techniques we use are related with the solution of boundary value problems associated to second order linear difffference equations. Consequently, we reduce the computational cost of the problem. In particular, we recover the inverses of some well known circulant matrices whose coeffifficients are arithmetic or geometric sequences, Horadam numbers among others. We also characterize when a general symme…

Determinants of Circulant Matrices with Some Certain Sequences

Let $\{a_k\}$ be a sequence of real numbers defined by an $m$th order linear homogenous recurrence relation. In this paper we obtain a determinant formula for the circulant matrix $A=circ(a_1, a_2, \cdots, a_n)$, providing a generalization of determinantal results in papers of Bozkurt \cite{Bozkurt}, Bozkurt and Tam \cite{BozkurtTam}, and Shen, et al. \cite{ShenCenHao}.

循环矩阵集合中的函数类及其特征刻画

Classes of functions in the set of circulant matrices and their characterization

本文引入取值于复元素循环矩阵集合的新函数类，将整函数等复变函数的特征定理扩展至多复变量循环矩阵代数结构，并推广了代数基本定理的变体。