Transvection conjugacy over a finite field

Every nonidentity transvection has an adapted basis in which it is $I+E_{12}$. Thus all such maps are conjugate in the general linear group. In dimension at least three, a scaling of a third basis vector centralizes this matrix and has arbitrary nonzero determinant; adjusting a conjugator by this scaling proves conjugacy in the special linear group as well.

// Target: algebra.bigb