On Bicomplex Representation Methods and
Application of Quaternion Range Hermitian
matrices (q-EP)

S. Sridevi; Dr.K. Gunasekaran

doi:https://doi.org/10.14445/22315373/IJMTT-V48P538

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 48 | Number 4 | Year 2017 | Article Id. IJMTT-V48P538 | DOI : https://doi.org/10.14445/22315373/IJMTT-V48P538

On Bicomplex Representation Methods and Application of Quaternion Range Hermitian matrices (q-EP)

S. Sridevi, Dr.K. Gunasekaran

Abstract

In this paper, a series of bicomplex representation methods of q-EP matrices is introduced. We present a new multiplication of q-EP matrices, a new determinant concept, a new inverse concept of q-EP matrix and a new similar matrix concept.

Keywords

q-EP matrix, q-EP determinant, Inverse of q-EP matrix, similar q-EP matrix.

References

[1] L. X. Chen, “Inverse Matrix and Properties of Double Determinant over Quaternion TH Field,” Science in China (Series A), Vol. 34, No. 5, 1991, pp. 25-35.
[2] L. X. Chen, “Generalization of Cayley-Hamilton Theorem over Quaternion Field,” Chinese Science Bulletin, Vol. 17, No. 6, 1991, pp. 1291-1293.
[3] R, M. Hou, X. Q. Zhao and l. T. Wang, “The Double Determinant of Vandermonde‟s Type over Quaternion Field,” Applied Mathematics and Mechanics, Vol. 20, No.9, 1999, pp. 100-107.
[4] L. P. Huang, “The Determinants of Quaternion Matrices and Their Properties,” Journal of Mathematics Study, Vol. 2, 1995, pp. 1-13.
[5] J. L. Wu, L. M. Zou, X. P. Chen and S. J. Li, “The Estimation of Eigen values of Sum, Difference, and Tensor Product of Matrices over Quaternion Division Algebra,” Linear Algebra and its Applications, Vol. 428, 2008, pp.3023-3033.
[6] T. S. Li, “Properties of Double Determinant over Quaternion Field,” Journal of Central China Normal University, Vol. 1, 1995, 3-7.
[7] B. X. Tu, “Dieudonne Determinants of Matrices over aDivision Ring,” Journal of Fudan University, 1990A, Vol.1, pp. 131-138.
[8] B. X. Tu, “Weak Direct Products and Weak Circular Product of Matrices over the Real Quaternion Division Ring,” Journal of Fudan University, Vol. 3, 1991, p. 337.
[9] J. L. Wu, “Distribution and Estimation for Eigenvalues of Real Quaternion Matrices,” Computers and Mathematics with Applications, Vol. 55, 2008, pp. 1998-2004.
[10] B. J. Xie, “Theorem and Application of Determinants Spread out of Self-Conjugated Matrix,” Acta Mathematica Sinica, Vol. 5, 1980, pp. 678-683.
[11] Q. C. Zhang, “Properties of Double Determinant over the Quaternion Field and Its Applications,” Acta MathematicaSinica, Vol. 38, No. 2, 1995, pp. 253-259.
[12] W. J. Zhuang, “Inequalities of Eigenvalues and Singular Values for Quaternion Matrices,” Advances in Mathematics, Vol. 4, 1988, pp. 403-406.
[13] W. Boehm, “On Cubics: A Survey, Computer Graphics and Image Processing,” Vol. 19, 1982, pp. 201-226.
[14] G. Farin, “Curves and Surfaces for Computer Aided Geometric Design,” Academic Press, Inc., San Diego CA, 1990.
[15] K. Shoemake, “Animating Rotation with QuaternionCalculus,” ACM SIGGRAPH, 1987, Course Notes, Computer Animation: 3–D Motion, Specification, and Control.
[16] Q. G. Wang, “Quaternion Transformation and Its Application to the Displacement Analysis of Spatial Mechanisms, Acta Mathematica Sinica, Vol. 15, No. 1, 1983, pp.54-61.
[17] G. S. Zhang, “Commutativity of Composition for Finite Rotation of a Rigid Body,” Acta Mechanica Sinica, Vol. 4, 1982.
[18] E. T. Browne, “The Characteristic Roots of a Matrix,” Bulletin of the American Mathematical Society, Vol. 36, 1930, pp. 705-710.
[19] J. L. Wu and Y. Wang, “A New Representation Theory and Some Methods on Quaternion Division Algebra,” Journal of Algebra, Vol. 14, No. 2, 2009, pp. 121-140.
[20] Q. W. Wang, “The General Solution to a System of Real Quaternion Matrix Equation,” Computer and Mathematicswith Applications, Vol. 49, 2005, pp. 665-675.
[21] G. B. Price, “An Introduction to Multicomplex Spaces and Functions,” Marcel Dekker, New York, 1991.
[22] D. Rochon, “A Bicomplex Riemann Zeta Function,” Tokyo Journal of Mathematics, Vol. 27, No. 2, 2004, pp.357-369.
[23] S. P. Goyal and G. Ritu, “The Bicomplex Hurwitz Zeta function,” The South East Asian Journal of Mathematics and Mathematical Sciences, 2006.
[24] S. P. Goyal, T. Mathur and G. Ritu, “Bicomplex Gamma and Beta Function,” Journal of Raj. Academy PhysicalSciences, Vol. 5, No. 1, 2006, pp. 131-142.
[25] J. N. Fan, “Determinants and Multiplicative Functionals on Quaternion Matrices,” Linear Algebra and Its Applications, Vol. 369, 2003, pp. 193-201.
[26]. Zhang.F, Quarternions and Matrices of quaternions, linear Algebra and its application, 251 (1997), 21 -57.
[27]. “Gunasekaran.K and Sridevi.S” On Range Quaternion Hermitian Matrices;Inter;J;Math.,Archieve-6(8), 159-163.
[28].“Gunasekaran.K and Sridevi.S” On Sums of Range Quaternion Hermitian Matrices; Inter;J.Modern Engineering Research -.5, ISS.11. 44 – 49(2015).
[29].“Gunasekaran.K and Sridevi.S” On Product of Range Quaternion Hermitian Matrices;Inter.,Journal of pure algebra – 6(6),2016,318 -321.
[30].“Gunasekaran.K and Sridevi.S” Generalized inverses , Group inverses and Revers order law of range quaternion matrices.,IOSR-JMVol.,12, Iss.4 ver.II(Jul – Aug 2016) ,51-55.
[31]. “Junliang Wu and Pingping Zhang” On Bicomplex Representation Methods and Applications of Matrices over Quaternionic Division Algebra, Advances in Pure Mathematics, 2011, 1, 9-15.

Citation :

S. Sridevi, Dr.K. Gunasekaran, "On Bicomplex Representation Methods and Application of Quaternion Range Hermitian matrices (q-EP)," International Journal of Mathematics Trends and Technology (IJMTT), vol. 48, no. 4, pp. 250-259, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V48P538