Why is it that the set of positive definite matrices is a convex cone? I'm having a bit of difficulty understanding this because through the definition of a cone, I am required to show that the conic combination belongs to the set $S$ ; $\forall$ $\theta$ $\geq 0$. But if I set $\theta = 0$ then will it not give a null matrix? If yes then it wont be positive definite anymore and will hence not belong to the set. Kindly let me know if my question doesnt make sense at any point, I'll try to elaborate my confusion more.
2026-05-16 10:12:59.1778926379
The set of Positive Definite Matrices is a Convex Cone
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