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For example, a [[homogeneous polynomial]] of degree {{mvar|k}} defines a homogeneous function of degree {{mvar|k}}.
The above definition extends to functions whose [[___domain of a function|___domain]] and [[codomain]] are [[vector space]]s over a [[Field (mathematics)|field]] {{mvar|F}}: a function <math>f : V \to W</math> between two {{mvar|F}}-vector
{{NumBlk|:|<math>f(s \mathbf{v}) = s^k f(\mathbf{v})</math>|{{EquationRef|1}}}}
for all nonzero <math>s \in F</math> and <math>v \in V.</math> This definition is often further generalized to functions whose ___domain is not {{mvar|V}}, but a [[cone (linear algebra)|cone]] in {{mvar|V}}, that is, a subset {{mvar|C}} of {{mvar|V}} such that <math>\mathbf{v}\in C</math> implies <math>s\mathbf{v}\in C</math> for every nonzero scalar {{mvar|s}}.
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