weighted homogeneous polynomial

Let 𝔽 be either the real or complex numbersMathworldPlanetmathPlanetmath.


Let p:𝔽n𝔽 be a polynomialMathworldPlanetmathPlanetmathPlanetmath in n variables and take integers d1,d2,,dn. The polynomial p is said to be weighted homogeneous of degree k if for all t>0 we have


The d1,,dn are called the weights of the variables x1,,xn.

Note that if d1=d2==dn=1 then this definition is the standard homogeneous polynomialMathworldPlanetmathPlanetmath.

Title weighted homogeneous polynomial
Canonical name WeightedHomogeneousPolynomial
Date of creation 2013-03-22 15:21:18
Last modified on 2013-03-22 15:21:18
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 5
Author jirka (4157)
Entry type Definition
Classification msc 12-00