SOLVING THE MATRIX INEQUALITY AXB plus (AXB)* >= C

• A pair of complex Hermitian matrices A and B of the same size are said to satisfy an inequality A >= B in the Lowner partial ordering if A-B is nonnegative definite. In this note, we first derive the general solutions in closed-form for the linear matrix equation AXB + (AXB)* = C by using generalized inverses of matrices, and then derive general solutions of the linear matrix inequality AXB + (AXB)* >= C when C is a Hermitian nonnegative definite matrix.

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NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

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