A. O. Isere

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 2, Pages 125–133

DOI: 10.7546/nntdm.2018.24.2.125-133

**Full paper (PDF, 155 Kb)**

## Details

### Authors and affiliations

A. O. Isere

*Department of Mathematics, Ambrose Alli University
Ekpoma 310001, Nigeria
*

### Abstract

A rhotrix is a rhomboidal array of numbers. In many respects, rhotrices are similar to matrices, and matrices, though, are of both even and odd dimensions but only rhotrices of odd dimension are well-known in literature. Even dimensional rhotrix has not been discussed. Therefore, this article introduces rhotrices with even dimension. These rhotrices are a special type of rhotrix where the heart has been extracted. Analysis, examples and some properties of these even-dimensional (heartless) rhotrices are presented and established as algebraic structures, mathematically tractable, and as a contribution to the concept of rhotrix algebra.

### Keywords

- Rhotrix
- Missing heart
- Even dimension
- Examples and operations

### 2010 Mathematics Subject Classification

- 15B99

### References

- Aashikpelokhai, U. S. U., Agbeboh, G. U., Uzor, J. E., Elakhe, A. O. & Isere, A. O. (2010) A first course in Linear Algebra and Algebraic structures, PON Publishers Ltd.
- Ajibade, A. O. (2003) The concept of Rhotrix in Mathematical Enrichment, International Journal of Mathematical Education in Science and Technology, 34 (2), 175–177.
- Aminu, A. & Michael, O. (2015) An introduction to the concept of paraletrix, a generalization of rhotrix, Journal of the African Mathematical Union, Springer-Verlag, 26 (5–6), 871–885.
- Atanassov, K. T. & Shannon, A. G. (1998) Matrix-Tertions and Matrix-Noitrets: Exercise for Mathematical Enrichment, International Journal Mathematical Education in Science and Technology, 29 (6), 898–903.
- Baumslag, B. & Chandler, B. (1968) Theory and Problems of Group Theory, Schaums Outline Series, McGraw-Hill.
- Ezugwu, E. A., Ajibade, A. O. & Mohammed, A. (2011) Generalization of Heart-oriented rhotrix Multiplication and its Algorithm Implementation, International Journal of Computer Applications, 13 (3), 5–11.
- Isere, A. O. (2016) Natural Rhotrix, Cogent Mathematics, 3 (1), Article 1246074.
- Isere, A. O. (2017) Note on classical and non-classical rhotrix, The Journal of the Mathematical Association of Nigeria, 44 (2), 119–124.
- Mohammed, A. (2009) A remark on the classifications of rhotrices as abstract structures, International Journal of Physical Sciences, 4 (9) 496–499.
- Mohammed, A. (2014) A new expression for rhotrix, Advances in Linear Algebra & Matrix Theory, 4, 128–133.
- Mohammed, A., Balarabe, M. & Imam, A. T. (2012) Rhotrix Linear Transformation, Advances in Linear Algebra & Matrix Theory, 2, 43–47.
- Mohammed, A. & Tella, Y. (2012) Rhotrix Sets and Rhotrix Spaces Category, International Journal of Mathematics and Computational Methods in Science and Technology, 2, 21–25.
- Sani, B. (2004) An alternative method for multiplication of rhotrices, International Journal of Mathematical Education in Science and Technology, 35, 777–781.
- Sani, B. (2007) The row–column multiplication for higher dimensional rhotrices, International Journal of Mathematical Education in Science and Technology, 38, 657–662.
- Sani, B. (2008) Conversion of a rhotrix to a coupled matrix, International Journal of Mathematical Education in Science and Technology, 39, 244–249.
- Tudunkaya, S. M, & Manjuola S. O. (2010) Rhotrices and the Construction of Finite Fields, Bull. Pure Appl Sci. Sect, E. Math. Stat, 29 (2), 225–229.
- Usaini, S. & Mohmmed, L. (2012) On the rhotrix eigenvalues and eigenvectors, Journal of the African Mathematical Union, Springer–Verlag, 25, 223–235.

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## Cite this paper

Isere, A. O. (2018). Even dimensional rhotrix. *Notes on Number Theory and Discrete Mathematics*, 24(2), 125-133, DOI: 10.7546/nntdm.2018.24.2.125-133.