On circulant like matrices properties involving Horadam, Fibonacci, Jacobsthal and Pell numbers

In this work a new type of matrix called circulant-like matrix is introduced. This type of matrix includes the classical k-circulant matrix, introduced in [4], in a natural sense. Its eigenvalues and its inverse and some other properties are studied, namely, it is shown that the inverse of a matrix...

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Bibliographic Details
Published in:Linear algebra and its applications 2021-05, Vol.617, p.100-120
Main Authors: Andrade, Enide, Carrasco-Olivera, Dante, Manzaneda, Cristina
Format: Article
Language:English
Subjects:
Eigenvalues
Fibonacci number
Fibonacci numbers
Horadam number
Jacobsthal number
k-circulant matrix
Linear algebra
Linear equations
Mathematical analysis
Pell number
Symmetric matrix
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Summary:In this work a new type of matrix called circulant-like matrix is introduced. This type of matrix includes the classical k-circulant matrix, introduced in [4], in a natural sense. Its eigenvalues and its inverse and some other properties are studied, namely, it is shown that the inverse of a matrix of this type is also a matrix of this type and that its first row is the unique solution of a certain system of linear equations. Additionally, for some of these matrices whose entries are written as function of Horadam, Fibonacci, Jacobsthal and Pell numbers we study its eigenvalues and write it as function of those numbers. Moreover, the same study is done if the entries are arithmetic sequences.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.01.016