The *congruence class of the solutions of some matrix equations

Authors:
Bing Zheng;Lijuan Ye;Dragana S. Cvetkovic-Ilic
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China;School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China;Department of Mathematics, Faculty of Sciences, University of Niš, Niš, Serbia
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

The *congruence class of a least square solution for the following matrix equations AX=B,A^*XA=D,AXB=Dand(AXXB)=(EF) is presented. Also, we derive necessary and sufficient conditions for the existence of a least square solution and present a general form of such solutions using the Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD).