Consider three symmetric, square, positive definite matrices (A, B, C), such that $$A\geq B.$$ (The positive semidefinite partial order is assumed) Can we conclude that $$(C+A)^{-1}*A\geq (C+B)^{-1}*B?$$ In the reals this is obvious, but I'm not sure if it extends to matrices.
2026-03-30 05:13:21.1774847601
Does $A\geq B$ imply $(C+A)^{-1}A\geq (C+B)^{-1}B$ for square positive definite matrices?
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