homogeneous function (original) (raw)

Definition 1.

Suppose V,W are a vector spaces over R, and f:V→W is a mapping.

• •
  If there exists an r∈ℝ, such that
  for all λ∈ℝ and v∈V, then f is a .
• •
  If there exists an r∈ℝ, such that
  for all λ∈ℝ and v∈V, then f is .
• •
  If there exists an r∈ℝ, such that
  for all λ≥0 and v∈V, then f is a .

Notes

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