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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 $n\times n$ matrices over the finite field $\mathbb F_{q^2}$ 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:

\begin{bmatrix} 0 & 1\\ 1 & 1 \end{bmatrix}

Does anyone know why this is and how I can easily rectify my computations so these matrices still preserve the Hermitian form $\langle x,x \rangle = x^*x$?

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 $n\times n$ matrices over the finite field $\mathbb F_{q^2}$ such that $U^* U = I$, where $U^*$ is the transpose of the matrix in which each component entry 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:

\begin{bmatrix} 0 & 1\\ 1 & 1 \end{bmatrix}

Does anyone know why this is and how I can easily rectify my computations so these matrices still preserve the Hermitian form $\langle x,x \rangle = x^*x$?