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

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## 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

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- Mohammed, A., & Okon, U. E. (2016). On subgroups of non-commutative general rhotrix group. Notes on Number Theory and Discrete Mathematics, 22(2), 72-90.
- Isere, A. O. (2019). Representation of higher even-dimensional rhotrix. Notes on Number Theory and Discrete Mathematics, 25(1), 206-219.
- Patil, K. M. (2021). Characterization of ideals of rhotrices over a ring and its applications. Notes on Number Theory and Discrete Mathematics, 27(1), 138-147.

## 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.