Suppose we have the following relationship, note that $A,B,C$ are closed convex matrix cones, $A^\ast=C,$ $B^\ast=C,$ can we state that $A=B$? Is the dual cone of a cone is unique? the definition ...
Is it possible to cover the cone of positive semidefinite matrices by a finite/countable/interesting family of closed intervals of matrices? How about a general convex cone? For the finite case the ...