derivative of homogeneous function
Theorem 1.
Suppose is a differentiable
positively homogeneous function of degree .
Then is a
positively homogeneous function of degree .
Proof.
By considering component functions if necessary, we can
assume that .
For , let be the
multiplication
map,
For and , we have
as claimed. ∎
Title | derivative of homogeneous function |
---|---|
Canonical name | DerivativeOfHomogeneousFunction |
Date of creation | 2013-03-22 14:45:05 |
Last modified on | 2013-03-22 14:45:05 |
Owner | matte (1858) |
Last modified by | matte (1858) |
Numerical id | 9 |
Author | matte (1858) |
Entry type | Theorem![]() |
Classification | msc 15-00 |