Structurally Stable Grassmann Transformations
Steve Batterson · Transactions of the American Mathematical Society · 1977
A Grassmann transformation is a diffeomorphism on a Grassmann manifold which is induced by an $n \times n$ nonsingular matrix. In this paper the structurally stable Grassmann transformations are characterized to be the maps which are induced by matrices whose eigenvalues have distinct moduli. There is exactly one topological conjugacy class of complex structurally stable Grassmann transformations. For the real case the topological classification is determined by the ordering (relative to modulus) of the signs of the eigenvalues of the inducing matrix.