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homogeneous function
In mathematics, a homogeneous function is a function with multiplicative scaling behaviour: if the argument is multiplied by a factor, then the result is multiplied by some power of this factor. More precisely, if is a function between two vector spaces over a field ''F'', and ''k'' is an integer, then ''ƒ'' is said to be homogeneous of degree ''k'' if
for all nonzero and . This implies it has scale invariance. When the vector spaces involved are over the real numbers, a slightly less general form of homogeneity is often used, requiring only that () hold for all α > 0.
Homogeneous functions can also be defined for vector spaces with the origin deleted, a fact that is used in the definition of sheaves on projective space in algebraic geometry. More generally, if ''S'' ⊂ ''V'' is any subset that is invariant under scalar multiplication by elements of the field (a "cone"), then a homogeneous function from ''S'' to ''W'' can still be defined by ().
==Examples==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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