Francisco Regis Vieira Alves and Paula Maria Machado Cruz Catarino

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 4, Pages 110—122

DOI: 10.7546/nntdm.2019.25.4.110-122

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## Details

### Authors and affiliations

Francisco Regis Vieira Alves

*Department of Mathematics, Federal Institute of Science and Education of Ceara
122, 13 de Maio, Brazil*

Paula Maria Machado Cruz Catarino

*Department of Mathematics, Universidade de Trás-os-Montes e Alto Douro
Quinta de Prados, Portugal
*

### Abstract

Recently Wani, Artaf, A., Badshah, V., Rathore, G. P. & Catarino introduced commutative matrices derived from the generalized Fibonacci matrix sequence and the *k*-Pell matrix sequence. In the present work, through the identification of certain special matrices, we can identify other forms of demonstration and also the description of commutative matrix properties for negative indices.

### Keywords

- Generalized Fibonacci matrix sequence
*k*-Pell matrix sequence

### 2010 Mathematics Subject Classification

- 11B37
- 11B39

### References

- Shannon, A. G., Horadam, A. & Anderson, P. G. (2006). The auxiliary equation associated with the plastic number. Notes on Number Theory and Discrete Mathematics. 12 (1), 1–12.
- Wani, A. A., Badshah, V., Rathore, G. P. & Catarino, P. M. (2019). Generalized Fibonacci and
*k*-Pell Matrix sequence, Journal of Mathematics, 51 (1), 17–28. - Turkmen, R. & Civciv, H. (2008). On the (
*s*,*t*)-Fibonacci and Fibonacci matrix sequence, Ars Combinatoria, 87, 161–173.

## Related papers

## Cite this paper

APAAlves, F. R. V. A., & Catarino, P. M. M. C. (2019). Generalized Fibonacci and *k*-Pell matrix sequences: Another way of demonstrating their properties. Notes on Number Theory and Discrete Mathematics, 25(4), 110-122, doi: 10.7546/nntdm.2019.25.4.110-122.

Alves, Francisco Regis Vieira and Paula Maria Machado Cruz Catarino. “Generalized Fibonacci and *k*-Pell Matrix Sequences: Another Way of Demonstrating Their Properties.” Notes on Number Theory and Discrete Mathematics 25, no. 4 (2019): 110-122, doi: 10.7546/nntdm.2019.25.4.110-122.

Alves, Francisco Regis Vieira and Paula Maria Machado Cruz Catarino. “Generalized Fibonacci and *k*-Pell Matrix Sequences: Another Way of Demonstrating Their Properties.” Notes on Number Theory and Discrete Mathematics 25.4 (2019): 110-122. Print, doi: 10.7546/nntdm.2019.25.4.110-122.