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Yongge Tian(yongge.tiangmail.com) Abstract: The inertia of a Hermitian matrix is defined to be a triplet composed by the numbers of the positive, negative and zero eigenvalues of the matrix counted with multiplicities, respectively. In this paper, we give various closedform formulas for the maximal and minimal values for the rank and inertia of the Hermitian expression $A + X$, where $A$ is a given Hermitian matrix and $X$ is a variable Hermitian matrix satisfying the range and rank restrictions ${\rm range}(X) \subseteq {\rm range}(B)$ and ${\rm rank}(X) \leqslant k$. Some expressions of the Hermitian matrix $X$ such that $A + X$ attains the extremal ranks and inertias are also presented. Keywords: Hermitian matrix expression; perturbation; rank; inertia; maximization; minimization; MoorePenrose inverse; equality; inequality Category 1: Global Optimization Category 2: Global Optimization (Theory ) Citation: Download: [PDF] Entry Submitted: 10/28/2010 Modify/Update this entry  
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