A function is homogeneous of degree when rescaling its arguments by a common scalar rescales its value by , whenever the arguments and that power are defined. For integer over a vector space, one can require every nonzero scalar; a homogeneous polynomial gives an example. On a domain stable under positive real rescaling, the positive-scaling version allows real . Degree-one positive homogeneity is the convention used for norms and many convex functions. The Euler theorem for homogeneous functions turns this scaling law into a differential identity for a differentiable function.
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