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MR2769881 (2012a:15018) 15A18 (15A23)
Liu, Yonghui; Tian, Yongge Max-min problems on the ranks and inertias of the matrix expressions $A-BXC\pm(BXC)\sp \ast$ with applications. J. Optim. Theory Appl. 148 (2011), no. 3, 593–622.
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