6. (20 points) Let (V.(. ) be a finite dimensional inner product space and let T:V V be a linear map. (a) (3 points) What coadition defines the adjoint map T V+V (b) (6 points) What is the relatioaship between the matrix represestation of T and T Take care to define (oe explain) all the relevaut terms in your expression (c) (3 points) Define what it means for T to be a normal operator. Contined froan Question 6 (d) (6 points) Consider VMax with its standard inner product and the linear map L Myx1 ? Mixt defined ly Lal!) = Ar for Deternine if L is normal (e) (2 points) What can you say about A in terms of diagonalizability