Rhotrix Linear Transformation

ABSTRACT

This paper considers rank of a rhotrix and characterizes its properties, as an extension of ideas to the rhotrix theory rhomboidal arrays, introduced in 2003 as a new paradigm of matrix theory of rectangular arrays. Furthermore, we present the necessary and sufficient condition under which a linear map can be represented over rhotrix.

This paper considers rank of a rhotrix and characterizes its properties, as an extension of ideas to the rhotrix theory rhomboidal arrays, introduced in 2003 as a new paradigm of matrix theory of rectangular arrays. Furthermore, we present the necessary and sufficient condition under which a linear map can be represented over rhotrix.

Cite this paper

A. Mohammed, M. Balarabe and A. Imam, "Rhotrix Linear Transformation,"*Advances in Linear Algebra & Matrix Theory*, Vol. 2 No. 4, 2012, pp. 43-47. doi: 10.4236/alamt.2012.24007.

A. Mohammed, M. Balarabe and A. Imam, "Rhotrix Linear Transformation,"

References

[1] A. O. Ajibade, “The Concept of Rhotrix in Mathematical Enrichment,” International Journal of Mathematical Education in Science and Technology, Vol. 34, No. 2, 2003, pp. 175-179. doi:10.1080/0020739021000053828

[2] K. T. Atanassov and A. G. Shannon, “Matrix-Tertions and Matrix-Noitrets: Exercise for Mathematical Enrichment,” International Journal of Mathematical Education in Science and Technology, Vol. 29, No. 6, 1998, pp. 898- 903.

[3] A. Aminu, “Rhotrix Vector Spaces,” International Journal of Mathematical Education in Science and Technology, Vol. 41, No. 4, 2010, pp. 531-573. doi:10.1080/00207390903398408

[4] A. Aminu, “The Equation Rnx = b over Rhotrices,” International Journal of Mathematical Education in Science and Technology, Vol. 41, No. 1, 2010, pp. 98-105. doi:10.1080/00207390903189187

[5] A. Mohammed, “Enrichment Exercises through Extension to Rhotrices,” International Journal of Mathematical Education in Science and Technology, Vol. 38, No. 1, 2007, pp. 131-136. doi:10.1080/00207390600838490

[6] A. Mohammed, “Theoretical Development and Applications of Rhotrices,” Ph.D. Thesis, Ahmadu Bello University, Zaria, 2011.

[7] B. Sani, “An Alternative Method for Multiplication of Rhotrices,” International Journal of Mathematical Education in Science and Technology, Vol. 35, No. 5, 2004, pp. 777-781. doi:10.1080/00207390410001716577

[8] B. Sani, “The Row-Column Multiplication of Higher Dimensional Rhotrices,” International Journal of Mathematical Education in Science and Technology, Vol. 38, No. 5, 2007, pp. 657-662.

[9] B. Sani, “Conversion of a Rhotrix to a ‘Coupled Matrix’,” International Journal of Mathematical Education in Science and Technology, Vol. 39, No. 2, 2008, pp. 244-249. doi:10.1080/00207390701500197

[1] A. O. Ajibade, “The Concept of Rhotrix in Mathematical Enrichment,” International Journal of Mathematical Education in Science and Technology, Vol. 34, No. 2, 2003, pp. 175-179. doi:10.1080/0020739021000053828

[2] K. T. Atanassov and A. G. Shannon, “Matrix-Tertions and Matrix-Noitrets: Exercise for Mathematical Enrichment,” International Journal of Mathematical Education in Science and Technology, Vol. 29, No. 6, 1998, pp. 898- 903.

[3] A. Aminu, “Rhotrix Vector Spaces,” International Journal of Mathematical Education in Science and Technology, Vol. 41, No. 4, 2010, pp. 531-573. doi:10.1080/00207390903398408

[4] A. Aminu, “The Equation Rnx = b over Rhotrices,” International Journal of Mathematical Education in Science and Technology, Vol. 41, No. 1, 2010, pp. 98-105. doi:10.1080/00207390903189187

[5] A. Mohammed, “Enrichment Exercises through Extension to Rhotrices,” International Journal of Mathematical Education in Science and Technology, Vol. 38, No. 1, 2007, pp. 131-136. doi:10.1080/00207390600838490

[6] A. Mohammed, “Theoretical Development and Applications of Rhotrices,” Ph.D. Thesis, Ahmadu Bello University, Zaria, 2011.

[7] B. Sani, “An Alternative Method for Multiplication of Rhotrices,” International Journal of Mathematical Education in Science and Technology, Vol. 35, No. 5, 2004, pp. 777-781. doi:10.1080/00207390410001716577

[8] B. Sani, “The Row-Column Multiplication of Higher Dimensional Rhotrices,” International Journal of Mathematical Education in Science and Technology, Vol. 38, No. 5, 2007, pp. 657-662.

[9] B. Sani, “Conversion of a Rhotrix to a ‘Coupled Matrix’,” International Journal of Mathematical Education in Science and Technology, Vol. 39, No. 2, 2008, pp. 244-249. doi:10.1080/00207390701500197