COMMON LEAST-RANK SOLUTION OF MATRIX EQUATIONS A₁X₁B₁=C₁ AND A₂X₂B₂=C_{2}WITH APPLICATIONS

Facta Universitatis. Series Mathematics and Informatics

Said Guedjiba¹  Sihem Guerarra² 

[1] Batna University;Oum El Bouaghi University

关键词: Matrix equation;    Rank formulas;    Moore Penrose Inverse;    Hermitia;    Least-rank solution.;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Nishu / University of Nis

【 摘 要 】

In this paper we will give the necessary and sufficient conditions for the paire of matrix equations A₁X₁B₁=C₁ and A₂X₂B₂=C_{2 }to have a common least-rank solution, and the expression of this solution is given, also we give the necessary and sufficient conditions for the matrix equation AXB=C to have a Hermitian least-rank solution. Using the first results, we investigate the expression of the general Hermitian least-rank solution of the matrix equation AXB=C.

【 授权许可】

Unknown