Hermitian transformation of T(A) = A*

65 Views Asked by At

I have a simple question in Linear Algebra -
What is the Hermitian-adjoint of the linear-transformation defined:

Over $M_n(\Bbb C)$ space, with the standard inner product $(A,B)_{st}$ := $tr(AB^*)$

$T(A)=A^*$

Find $T^*$ that satisfies $(TA,B)_{st} = (A,T^*B)_{st}$ for all $A,B\in M_n\Bbb C$