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Yongge Tian(yongge.tiangmail.com) Abstract: For a given linear matrix function $A_1  B_1XB^*_1$, where $X$ is a variable Hermitian matrix, this paper derives a group of closedform formulas for calculating the global maximum and minimum ranks and inertias of the matrix function subject to a pair of consistent matrix equations $B_2XB^*_2 = A_2$ and $B_3XB_3^* = A_3$. As applications, we give necessary and sufficient conditions for the triple matrix equations $B_1XB^*_1 =A_1$, $B_2XB^*_2 = A_2$ and $B_3XB^*_3 = A_3$ to have a common Hermitian solution. In addition, we discuss the global optimizations on the rank and inertia of the common Hermitian solution of the pair of matrix equations $B_2XB^*_2 = A_2$ and $B_3XB^*_3 = A_3$. Keywords: Matrix function; matrix equation; common Hermitian solution; rank; inertia; maximization; minimization; L\"owner partial ordering Category 1: Global Optimization (Theory ) Citation: Download: [PDF] Entry Submitted: 04/10/2011 Modify/Update this entry  
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