homogeneous function


Definition 1.

Suppose V,W are a vector spacesMathworldPlanetmath over R, and f:VW is a mapping.

  • If there exists an r, such that

    f(λv)=λrf(v)

    for all λ and vV, then f is a .

  • If there exists an r, such that

    f(λv)=|λ|rf(v)

    for all λ and vV, then f is .

  • If there exists an r, such that

    f(λv)=λrf(v)

    for all λ0 and vV, then f is a .

Notes

For any homogeneous functionMathworldPlanetmath as above, f(0)=0.

When the of homegeneity is clear one simply talks about r-homogeneous functions.

Title homogeneous function
Canonical name HomogeneousFunction
Date of creation 2013-03-22 14:44:37
Last modified on 2013-03-22 14:44:37
Owner matte (1858)
Last modified by matte (1858)
Numerical id 8
Author matte (1858)
Entry type Definition
Classification msc 15-00
Synonym positively homogeneous function of degree
Synonym homogeneous function of degree
Synonym positively homogeneous function
Related topic HomogeneousPolynomial
Related topic SubLinear