Year: 1966
Type: article
Abstract: In generalizing Grace's Theorem on apolar polynomials, it was convenient (see reference 1) to use a set of relations among the coefficients of a pair of polynomials which is invariant under nonsingular linear transformations of the polynomials.Other invariant relations among their coefficients will define other classes of pairs of polynomials.The present paper establishes a set of relations which is both necessary and sufficient to guarantee that two polynomials of degree n either have a common zero of multiplicity at least n -1 or have their zeros all lying on one circle and so related that if the zeros of one polynomial are transformed, by a linear transformation, into the nth.roots of +1 then the zeros of the other are carried, by the same transformation, into the nth roots of -1.
Source: Pacific Journal of Mathematics
Author: Ruth Goodman
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2027468897