Say that one has a matrix representation of an operator A with differential operators as entries in the matrix A.
Is this a non-linear matrix? Since the differential is a linear operator and A is composed of linear operators, I'm leaning towards A being a linear operator.
If one were to take the conjugate transpose of A, would the differential operators be modified? I'm trying to prove that A is anti-hermitian, and it seems to me that the differential operators would have to be negated when A is conjugate-transposed in order for A to be anti-hermitian.