On Tri Complex Representation Methods of a Quaternion Matrix Trace Inequality

K. Gunasekaran; M.Rahamathunisha

doi:https://doi.org/10.14445/22315373/IJMTT-V49P552

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 49 | Number 6 | Year 2017 | Article Id. IJMTT-V49P552 | DOI : https://doi.org/10.14445/22315373/IJMTT-V49P552

On Tri Complex Representation Methods of a Quaternion Matrix Trace Inequality

K. Gunasekaran, M.Rahamathunisha

Abstract

In this note, the matrix trace inequality for positive semi definite quaternion matrices A and B,𝑡𝑟 𝐴 ∗ 𝐵 𝑚 ≤ 𝑡𝑟 𝐴 2𝑚 ∗ 𝑡𝑟 𝐵 2𝑚 1/2 is established, where m is an integer. The above inequality for improves the result given by yang (J. Math Anal Appl. 250 (2000), 372 – 374).

Keywords

Product of quaternion matrix, Positive semi definite, Positive definite, Hermitian matrix.

References

1. Gunasekaran. K. and Rahamathunisha. M: “On tricomplex representation methods and application of matrices over quaternion division algebra”; Applied Science Periodical. Volume XVIII, No.1, Feb (2016).
2. Gunasekaran. K, Kannan. K and Rahamathunisha. M: “On Tri Complex representation methods of Matrix trace inequality”; Journal of ultra scientist of physical sciences. http://dx.doi.org/10.22147/jusps-A/290105, JUSPS –A Vol.29(1), 30-32 (2017).
3. Horn. R.A. and Johnson. C.R: “Topics in Matrix Analysis”; pp. 171-172, Cambridge Univ. Press, Cambridge, UK. (1991).
4. Mitrinovic. D.S: “Analytic Inequalities”; pp.52 and 165, Springer-Verlag, New York, 1970.
5. Yang. X: “A Matirx trace inequality”; J. Math. Anal. Appl. 250, 372-374 (2000).

Citation :

K. Gunasekaran, M.Rahamathunisha, "On Tri Complex Representation Methods of a Quaternion Matrix Trace Inequality," International Journal of Mathematics Trends and Technology (IJMTT), vol. 49, no. 6, pp. 325-330, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V49P552