  Hurwitz transformations are defined as specific automorphisms of a
Cayley-Dickson algebra. These transformations generate quadratic and
nonquadratic forms. We investigate here the Hurwitz transformations
corresponding to Cayley-Dickson algebras of dimensions 2m = 2, 4 and 8. The
Hurwitz transformations which lead to quadratic forms are discussed from
geometrical and Lie-algebraic points of view. Applications to number theory and
dynamical systems are briefly examined.
