Homogeneous function: Difference between revisions

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{{More footnotes|date=July 2018}}

{{for|homogeneous linear maps|Graded vector space#Homomorphisms}}

In [[mathematics]], a '''homogeneous function''' is a [[function of several variables]] such that, ifthe allfollowing itsholds: If each of the function's arguments areis multiplied by athe same [[scalar (mathematics)|scalar]], then itsthe function's value is multiplied by some power of this scalar,; the power is called the '''degree of homogeneity''', or simply the ''degree'';. thatThat is, if {{mvar|k}} is an integer, a function {{mvar|f}} of {{mvar|n}} variables is homogeneous of degree {{mvar|k}} if

:<math>f(sx_1,\ldots, sx_n)=s^k f(x_1,\ldots, x_n)</math>

for every <math>x_1, \ldots, x_n,</math> and <math>s\ne 0.</math>