COMMON HERMITIAN LEAST-RANK SOLUTION OF MATRIX EQUATIONS $A_{1}X_{1}A_{1}^*=B_{1}$ AND $A_{2}X_{2}A_{2}^*=B_{2}$ SUBJECT TO INEQUALITY RESTRICTIONS

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 generalized inverse;    Hermitian;    Least-rank solution;    Inertia.;   

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 establish a set of explicite formulas for calculating the maximal and minimal ranks and inertias of P-X with respect to X, where P∈ℂ_{H}ⁿ is given, X is a common Hermitian least-rank solution to matrix equations A₁XA₁^{∗}=B₁ and A₂XA₂^{∗}=B₂. As applications, we drive necessary and sufficient conditions for X≻P(≥P, ≺P, ≤P) in the löwner partial ordering. As consequence, we give necessary and sufficient conditions for the existence of common Hermitian positive (nonnegative, negative, nonpositive) definite least-rank solution to A₁XA₁^{∗}=B₁ and A₂XA₂^{∗}=B₂.

【 授权许可】

Unknown