In fact, I would say that there are serious reasons why transposing IS is conjugate . Consider the matrix representation of complex numbers. Let be
I = (1 0) J = (0 -1) (0 1) (1 0)
and note that transposing J ( J^T ) is simply -J. Then we have this equivalence (using j to denote the imaginary unit):
x + yj <---> xI + yJ (x + yj)* <---> xI - yJ = (xI + yJ)^T
Thus, conjugation of a complex number was the same operation as the transfer of its matrix representation. What happens if we have a matrix nxn complex numbers? Why then can we simply imagine it as a 2nx2n matrix of real numbers, where each 2x2 submatrix has the form xI + yJ ! It turns out that if you make the Hermitian (conjugate) transposed complex matrix nxn just equivalent to ordinary transposition in real form 2nx2n . In fact, I will go further and say (without proof) that any vector or matrix over complex numbers has an isomorphism in vectors / matrices over actions (the latter has double dimension) and that the conjugate transposition in the complex version is identical to the transposition in the real version.
With that in mind, I would say that the “normal transposition” of a matrix over complex numbers is actually a very strange thing. No wonder we do not find it in natural laws!
If you like, the natural representation is the real 2nx2n form. It so happened that, for historical reasons, we first developed an algebraic form using the symbols j or i , and came up with the idea of conjugation, which is actually just a special case of transposition.
Therefore, when you transfer the matrix over complex numbers, Matlab successfully completes, matching the elements for you.
If you want to know more, it's worth reading about representation theory. Wikipedia is a good start, although I think their article is a bit technical: https://en.wikipedia.org/wiki/Representation_theory