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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 457298, 7 pages
http://dx.doi.org/10.1155/2014/457298
Research Article

On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction

Department of Mathematics and Computational Science, Huainan Normal University, Anhui 232038, China

Received 16 February 2014; Revised 11 June 2014; Accepted 22 June 2014; Published 8 July 2014

Academic Editor: Sofiya Ostrovska

Copyright © 2014 Hongxing Wang and Yeguo Sun. 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

We discuss the feasible interval of the parameter and a general expression of matrix which satisfies the rank equation . With these results, we study two problems under the rank constraint . The first one is to determine the maximal and minimal ranks under the rank constraint . The second one is to derive the least squares solutions of under the rank constraint .