homogeneous polynomial

A polynomialMathworldPlanetmathPlanetmathPlanetmath P(x1,,xn) of degree k is called homogeneousPlanetmathPlanetmathPlanetmath if P(cx1,,cxn)=ckP(x1,,xn) for all constants c.

An equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath definition is that all terms of the polynomial have the same degree (i.e. k).

Observe that a polynomial P is homogeneous iff degP=ordP.

As an important example of homogeneous polynomialsMathworldPlanetmathPlanetmath one can mention the symmetric polynomialsMathworldPlanetmath.

Title homogeneous polynomial
Canonical name HomogeneousPolynomial
Date of creation 2013-03-22 13:21:11
Last modified on 2013-03-22 13:21:11
Owner jgade (861)
Last modified by jgade (861)
Numerical id 11
Author jgade (861)
Entry type Definition
Classification msc 12-00