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## Main Question or Discussion Point

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?

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?