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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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When the summands of a positive definite matrix are positive definite

Let $A,B$ be two real symmetric matrices. Let $C = A+B$ be a positive-definite matrix. Write $C>0$ for $C$ being positive-definite. Suppose that $A>0 \implies C>0$ and $B > 0 \implies C>0$, can anythi …