Say that one has a matrix representation of an operator
A with differential operators as entries in the matrix
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.