Let us consider the set S n + of symmetric positive semidefinite matrices nxn. It is easy

Let us consider the set Sⁿ₊ of symmetric positive semidefinite matrices

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nxn. It is easy to see that this is a convex cone. Indeed, if Q1, Q2 S, i.e., they satisfy the condition xQx > 0, for any x and i = 1, 2, then Q1 + A2Q2 S2, for any A1, A2 0. In par- ticular, this holds when the non-negative weights add up to 1, which implies convexity. To streamline notation, we often write Q 0 rather than Q = ST.