F X Y Y Inv X Y Dom F X Y X X Gt 0 Is F Convex

f(X,y)=y’*inv(X)*y, dom f={(X,y)|X+x’>0}. is f convex? If not give a simple counterexample.I can proof convexity when X is restricted to Sn via its epigraph but I don’t know how to explain the general convexity of f for any X. Any help would be appreciated.

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