Gowda, M. Seetharama2022-10-072022-10-072021-10-14http://hdl.handle.net/11603/26116On a finite dimensional real vector space V, we consider a real homogeneous polynomial p of degree n that is hyperbolic relative to a vector e ∈ V. This means that p(e) 6= 0 and for any (fixed) x ∈ V, the roots of the one-variable polynomial t 7→ p(te − x) are all real. Let λ(x) denote the vector in Rn whose entries are these real roots written in the decreasing order. Relative to the map λ : V → Rn, we introduce and study automorphisms, majorization, and doubly stochastic transformations16 pagesen-USThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.Text