Question: 8. () (a) Let T : Mnn R denote the trace map: T(A) = tr A for all A Mnn . Show that T is

8. () (a) Let T : Mnn R denote the trace map: T(A) = tr A for all A Mnn . Show that T is linear and dim(ker T) = n 2 1.

(b) Show that the transformation F : Mmn Mnm defined by F(A) = AT is a linear isomorphism

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