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Journal of Applied Mathematics
Volume 2014, Article ID 857081, 9 pages
http://dx.doi.org/10.1155/2014/857081
Research Article

Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix Equation with the Least Norm

School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China

Received 5 December 2013; Accepted 3 February 2014; Published 15 April 2014

Academic Editor: Qing-Wen Wang

Copyright © 2014 Shi-Fang Yuan. 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

Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the least norm, and least squares real solution with the least norm of the quaternion matrix equation , respectively.