On r-circulant matrices with Horadam numbers having arithmetic indices

Aldous Cesar F. Bueno
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 2, Pages 177–197
DOI: 10.7546/nntdm.2020.26.2.177-197
Full paper (PDF, 238 Kb)

Details

Authors and affiliations

Aldous Cesar F. Bueno
Mathematics Unit, Philippine Science High School – Central Luzon Campus
Lily Hill, Clark Freeport Zone, Pampanga, Philippines

Abstract

We investigate an r-circulant matrix whose entries are Horadam numbers having arithmetic indices. We then solve for the eigenvalues, determinant, Euclidean norm and spectral norm of the matrix. Lastly, we present some special cases and some results on identities and divisibility.

Keywords

• Horadam Numbers
• r-circulant matrix
• Eigenvalue
• Determinant
• Euclidean norm
• Spectral norm

2010 Mathematics Subject Classification

• 11B05
• 15B36
• 11B39

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