Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-19T21:02:43.558Z Has data issue: false hasContentIssue false
  • English
  • Français

Further Solutions of a Yang-Baxter-like Matrix Equation

Published online by Cambridge University Press:  28 May 2015

Jiu Ding ,
Chenhua Zhang  and
Noah H. Rhee
Jiu Ding*
Affiliation:
Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406-5045, USA
Chenhua Zhang*
Affiliation:
Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406-5045, USA
Noah H. Rhee*
Affiliation:
Department of Mathematics and Statistics, University of Missouri - Kansas City, Kansas City, MO 64110-2499, USA
*
Corresponding author. Email Address: Jiu.Ding@usm.edu
Corresponding author. Email Address: Chenhua.Zhang@usm.edu
Corresponding author. Email Address: RheeN@umkc.edu
Get access

Abstract

The Yang-Baxter-like matrix equation AXA = XAX is reconsidered, and an infinite number of solutions that commute with any given complex square matrix A are found. Our results here are based on the fact that the matrix A can be replaced with its Jordan canonical form. We also discuss the explicit structure of the solutions obtained.

Keywords

15A18Matrix equationJordan canonical formprojector
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 4 , November 2013 , pp. 352 - 362
Copyright
Copyright © Global-Science Press 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Atiyah, M., Geometry, topology and physics, Quart. J. Roy. Astr. Soc. 29, 287–299 (1988).Google Scholar
[2]Baxter, R.J., Partition function of the eight-vertex lattice model, Ann. Phys. 70, 193–228 (1972).CrossRefGoogle Scholar
[3]Cibotarica, A., Ding, J., Kolibal, J. and Rhee, N., Solutions of the Yang-Baxter matrix equation for an idempotent, NACO 3, 347–352 (2013).Google Scholar
[4]Cullen, C., Matrices and Linear Transformations, Dover (1990).Google Scholar
[5]Ding, J. and Rhee, N., A nontrivial solution to a stochastic matrix equation, East Asian J. App. Math. 2, 277–284 (2012).Google Scholar
[6]Ding, J. and Rhee, N., Spectral solutions of the Yang-Baxter matrix equation, J. Math. Anal. Appl. 402, 567–573 (2013).Google Scholar
[7]Faddeev, L.D., History and perspectives of quantum groups, Milan J. Math. 74, 279–294 (2006).Google Scholar
[8]Felix, F., Nonlinear Equations, Quantum Groups and Duality Theorems: A Primer on the Yang-Baxter Equation, VDM Verlag (2009).Google Scholar
[9]Yang, C.N., Some exact results for the many-body problem in one dimension with repulsive delta-function interaction, Phys. Rev. Lett. 19, 1312–1315 (1967).Google Scholar
[10]Yang, C. and Ge, M., Braid Group, Knot Theory, and Statistical Mechanics, World Scientific (1989).Google Scholar