Consider the following statement Let T (size: nxm) be a complex matrix. Then if A of dimension nxn is positive semidefinite then T*AT >= 0. Now I was wondering if the converse is true aswel? In my math book they used the converse statement to proof something, but is it possible to say that if T*AT >= 0 (positive semidefinite) then A>= 0? Note: I used the symbol * to indicate the Hermittian. Someone got some tips for me?