On solutions of the matrix equation AX=B with respect to semi-tensor product. Issue 5 (March 2016)

• Record Type: Journal Article
• Authors: Yao, Juan; Feng, Jun-e; Meng, Min
• Is Part Of: Journal of the Franklin Institute. Volume 353:Issue 5(2016:Mar.)
• Page Start: 1109
• Page End: 1131
• Publication Date: 2016-03
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2015.04.004
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: This paper studies the solutions of the matrix equation AX = B with respect to semi-tensor product. Firstly, the matrix–vector equation AX = B with semi-tensor product is discussed. Compatible conditions are established for the matrices, and a necessary and sufficient condition for the solvability of the matrix–vector equation is proposed. In addition, concrete solving methods are provided. Based on this, the solvability of the matrix equation AX = B with semi-tensor product is studied, and several examples are presented to illustrate the efficiency of the results.