Journal of Applied Mathematics
Volume 2013 (2013), Article ID 230408, 6 pages
http://dx.doi.org/10.1155/2013/230408
Research Article

Left and Right Inverse Eigenpairs Problem for -Hermitian Matrices

Fan-Liang Li,1 Xi-Yan Hu,2 and Lei Zhang2

1Institute of Mathematics and Physics, School of Sciences, Central South University of Forestry and Technology, Changsha 410004, China
2College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

Received 6 December 2012; Accepted 20 March 2013

Academic Editor: Panayiotis J. Psarrakos

Copyright © 2013 Fan-Liang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Left and right inverse eigenpairs problem for -hermitian matrices and its optimal approximate problem are considered. Based on the special properties of -hermitian matrices, the equivalent problem is obtained. Combining a new inner product of matrices, the necessary and sufficient conditions for the solvability of the problem and its general solutions are derived. Furthermore, the optimal approximate solution and a calculation procedure to obtain the optimal approximate solution are provided.