If you have a matrix of variables say $X=AA^{T}$ which by definition must be either positive definite or positive semidefinite, and you have some function $f(X)$, as $X \in C$, where $C$ is a cone, can you say that $f(X)$ is a convex function for any $f:C \rightarrow \mathbb{R} $?
2026-03-29 21:36:05.1774820165
Is the function of a positive (semi) definite matrix convex?
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