Abstract:We consider the extremal inertias and ranks of the matrix expressionsf(X,Y)=A3-B3X-(B3X)*-C3YD3-(C3YD3)*, whereA3=A3*, B3, C3, andD3are known matrices andYandXare the solutions to the matrix equationsA1Y=C1,YB1=D1, andA2X=C2, respectively. As applications, we present necessary and sufficient condition for the previous matrix functionf(X,Y)to be positive (negative), non-negative (positive) definite or nonsingular. We also characterize the relations between the Hermitian part of the solutions of the above-ment… Show more
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