Spaces of similarities. IV. (<i>s,t</i>)-families

Abstract

The determination of spaces of similarities is a generalization of the Hurwitz problem of compasition of quadratic forms. For forms , q over the field F, we write < Sim (q) if q admits composition with . When F is the real or complex field, the possible dimensions of and q were determined long ago by Radon and Hurwitz. We show that these classical bounds are still correct over any field F of characteristic not 2.