Journal of Applied Mathematics
Volume 2013 (2013), Article ID 271978, 5 pages
http://dx.doi.org/10.1155/2013/271978
Research Article

Completing a Block Matrix of Real Quaternions with a Partial Specified Inverse

Yong Lin1,2 and Qing-Wen Wang1

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China

Received 4 December 2012; Revised 23 February 2013; Accepted 20 March 2013

Academic Editor: K. Sivakumar

Copyright © 2013 Yong Lin and Qing-Wen Wang. 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

This paper considers a completion problem of a nonsingular block matrix over the real quaternion algebra : Let be nonnegative integers, , and be given. We determine necessary and sufficient conditions so that there exists a variant block entry matrix such that is nonsingular, and is the upper left block of a partitioning of . The general expression for is also obtained. Finally, a numerical example is presented to verify the theoretical findings.