So I would love to utilize the unitary group feature in Sage; however, it does not seem like Sage defines this group in the standard way that I have seen, namely n×n matrices over the finite field Fq2 such that U∗U=I, where U∗ is the transpose of the matrix in which each component of U is raised to the q power.
For some weird reason it appears as though sage uses the antitranspose instead of the traditional transpose operation to define unitary matrices, since the following matrix, for example, is included:
[0111]
Does anyone know why this is and how I can easily rectify my computations so these matrices still preserve the Hermitian form ⟨x,x⟩=x∗x?