First Review of Articles on Rhotrix Theory Since Its Inception ()

A. Mohammed^{*}, M. Balarabe^{}

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria.

**DOI: **10.4236/alamt.2014.44020
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Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria.

This paper presents an up-to-date review of the developments made in the field of rhotrix theory for a decade, starting from the year 2003, when the concept of rhotrix was introduced, up to the end of 2013. Over forty articles on rhotrix theory have been published in journals since its inception, indicating the need for a first review.

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Mohammed, A. and Balarabe, M. (2014) First Review of Articles on Rhotrix Theory Since Its Inception. *Advances in Linear Algebra & Matrix Theory*, **4**, 216-224. doi: 10.4236/alamt.2014.44020.

Conflicts of Interest

The authors declare no conflicts of interest.

[1] |
Ajibade, A.O. (2003) The Concept of Rhotrix in Mathematical Enrichment. International Journal of Mathematical Education in Science and Technology, 34, 175-179. http://dx.doi.org/10.1080/0020739021000053828 |

[2] | Atanassov, K.T. and Shannon, A.G. (1998) Matrix-Tertions and Matrix-Noitrets: Exercises in Mathematical Enrichment. International Journal of Mathematical Education in Science and Technology, 29, 898-903. |

[3] |
Sani, B. (2004) An Alternative Method for Multiplication of Rhotrices. International Journal of Mathematical Education in Science and Technology, 35, 777-781. http://dx.doi.org/10.1080/00207390410001716577 |

[4] |
Sani, B. (2007) The Row-Column Multiplication of Higher Dimensional Rhotrices. International Journal of Mathematical Education in Science and Technology, 38, 657-662. http://dx.doi.org/10.1080/00207390601035245 |

[5] | Mohammed, A. (2011) Theoretical Development and Applications of Rhotrices. Ph.D. Thesis, Ahmadu Bello University, Zaria. |

[6] |
Mohammed, A. (2007) Enrichment Exercises through Extension to Rhotrices. International Journal of Mathematical Education in Science and Technology, 38, 131-136. http://dx.doi.org/10.1080/00207390600838490 |

[7] | Mohammed, A. (2007) A Note on Rhotrix Exponent Rule and Its Applications to Special Series and Polynomial Equations Defined over Rhotrices. Notes on Number Theory and Discrete Mathematics, 13, 1-15. |

[8] | Mohammed, A. (2009) A Remark on the Classifications of Rhotrices as Abstract Structures. International Journal of Physical Sciences, 4, 496-499. |

[9] | Usaini, S. and Tudunkaya, S.M. (2011) Certain Field of Fractions. Global Journal of Science Frontier Research, 11, 4-8. |

[10] | Usaini, S. and Tudunkaya, S.M. (2012) Note on Certain Field of Fractions. Global Journal of Science Frontier Research, 12, 74-81. |

[11] | Mohammed, A., Ezugwu, E.A. and Sani, B. (2011) On Generalization and Algorithmatization of Heart-Based Method for Multiplication of Rhotrices. International Journal of Computer Information Systems, 2, 46-49. |

[12] | Absalom, E.A., Junaidu, S.B. and Sani, B. (2011) The Concept of Heart-Oriented Rhotrix Multiplication. Global Journal of Science Frontier, 11, 35-46. |

[13] | Mohammed and Tijjani (2011) Rhotrix Topological Spaces. International Journal of Advances in Science and Technology, 3. |

[14] | Mohammed, A. and Sani, B. (2011) On Construction of Rhomtrees as Graphical Representation of Rhotrices. Notes on Number Theory and Discrete Mathematics, 17, 21-29. |

[15] | Tudunkaya and Makanjuola (2010) Algebraic Properties of Singleton, Coiled and Modulo Rhotrices. African Journal of Mathematics and Computer Sciences. |

[16] | Tudunkaya, S.M. and Makanjuola, S.O. (2010) Rhotrices and the Construction of Finite Fields. Bulletin of Pure and Applied Sciences, 29e, 225-229. |

[17] | Usaini, S. and Tudunkaya, S.M. (2011) Note on Rhotrices and the Construction of Finite Fields. Bulletin of Pure and Applied Sciences, 30e, 53-59. |

[18] | Tudunkaya, S.M. and Makanjuola, S.O. (2012) On the Structure of Rhotrices. National Association of Mathematical Physics, 21, 271-280. |

[19] | Tudunkaya, S.M. and Makanjuola, S.O. (2012) Certain Quadratic Extensions. National Association of Mathematical Physics, 21, 271-280. |

[20] | Tudunkaya, S.M. (2013) Rhotrix Polynomial and Polynomial Rhotrices. Pure and Applied Mathematics Journal, 2, 38-41. http://dx.doi.org/10.11648/j.pamj.20130201.16 |

[21] | Mohammed, A. and Tella, Y. (2012) Rhotrix Sets and Rhotrix Spaces Category. International Journal of Mathematics and Computational Methods in Science and Technology, 2, 21-25. |

[22] | Aminu, A. (2009) On the Linear System over Rhotrices. Notes on Number Theory and Discrete Mathematics, 15, 7-12. |

[23] | Aminu, A. (2012) A Note on the Rhotrix System of Equation. Journal of the Nigerian Association of Mathematical Physics, 21, 289-296. |

[24] | Kaurangini, M.L. and Sani, B. (2007) Hilbert Matrix and Its Relationship with a Special Rhotrix. Journal of the Mathematical Association of Nigeria, 34, 101-106. |

[25] | Sani, B. (2008) Conversion of a Rhotrix to a Coupled Matrix. International Journal of Mathematical Education in Science and Technology, 39, 244-249. http://dx.doi.org/10.1080/00207390701500197 |

[26] | Sani, B. (2009) Solution of Two Coupled Matrices. Journal of the Mathematical Association of Nigeria, 32, 53-57. |

[27] | Aminu, A. (2010) The Equation Rnx = b over Rhotrices. International Journal of Mathematical Education in Science and Technology, 41, 98-105. http://dx.doi.org/10.1080/00207390903189187 |

[28] | Aminu, A. (2010) Rhotrix Vector Spaces. International Journal of Mathematical Education in Science and Technology, 41, 531-578. http://dx.doi.org/10.1080/00207390903398408 |

[29] |
Aminu, A. (2010) An Example of Linear Mappings: Extension to Rhotrices. International Journal of Mathematical Education in Science and Technology, 41, 691-698. http://dx.doi.org/10.1080/00207391003605213 |

[30] | Absalom, E.E., Ajibade, A.O. and Sahalu, J.B. (2011) Algorithm Design for Row-Column Multiplication of N-Dimensional Rhotrices. Global Journal of Computer Science and Technology, 11, 22-30. |

[31] | Chinedu, M.P. (2012) Row-Wise Representation of Arbitrary Rhotrix. Notes on Number Theory and Discrete Mathematics, 18, 1-27. |

[32] | Sharma, P.L. and Kanwar, R.K. (2012) The Cayley-Hamilton Theorem for Rhotrices. International Journal of Mathematics and Analysis, 4, 171-178. |

[33] | Aminu, A. (2012) Cayley-Hamilton Theorem in Rhotrices. National Association of Mathematical Physics, 20, 289-296. |

[34] | Sharma, P.L. and Kanwar, R.K. (2011) A Note on Relationship between Invertible Rhotrices and Associated Invertible Matrices. Bulletin of Pure and Applied Sciences: Mathematics and Statistics, 30e, 333-339. |

[35] | Sharma, P.L. and Kanwar, R.K. (2012) Adjoint of a Rhotrix and Its Basic Properties. International Journal of Mathematical Sciences, 11, 337-343. |

[36] | Sharma, P.L. and Kanwar, R.K. (2012) On Inner Product Spaces and Bilinear Forms of Rhotrices. Bulletin of Pure and Applied Sciences, 31e, 109-118. |

[37] | Aminu, A. (2012) A Determinant Method for Solving Rhotrix System of Equation. Journal of the Nigerian Association of Mathematical Physics, 21, 281-288. |

[38] | Usaini, S. (2012) On the Construction of Involutory Rhotrices. International Journal of Mathematical Education in Science and Technology, 43, 510-515. http://dx.doi.org/10.1080/0020739X.2011.599875 |

[39] | Sharma, P.L. and Kanwar, R.K. (2013) On Involutory and Pascal Rhotrices. International Journal of Mathematical Sciences and Engineering Applications, 7, 133-146. |

[40] | Aminu, A. and Michael, O. (2013) Adjacent Rhotrix of a Complete, Simple and Undirected Graph. National Association of Mathematical Physics, 25, 267-274. |

[41] | Absalom, E.A., Abdullahi, M., Ibrahim, K., Mohammed, A. and Junaidu, S.B. (2011) Parallel Multiplication of Rhotrices Using Systolic Array Architecture. International Journal of Computer Information Systems, 2, 68-73. |

[42] |
Absalom, E.E. and Sahalu, J.B. (2012) Rhotrix Multiplication of Two-Dimensional Process Grid Topologies. International Journal of Grid and High Performance Computing, 4, 21-36. http://dx.doi.org/10.4018/jghpc.2012010102 |

[43] | Mohammed, A., Balarabe, M. and Imam, A.T. (2012) Rhotrix Linear Transformation. Advances in Linear Algebra & Matrix Theory, 2, 43-47. http://dx.doi.org/10.4236/alamt.2012.24007 |

[44] | Usaini, S. (2012) Rhotrices and Elementary Row Operation. Journal of the Nigerian Association of Mathematical Physics, 20, 37-42. |

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