(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A function F of n real variables is called homogeneous of degree r if it satisfies

F(tx_1, tx_2, ..., tx_n) = (t^r)F(x_1,x_2,...,x_n)

By differentiation with respect to t, show that a function F is an eigenfunction of the operator:

x^1 ∂/∂x_1 + ... + x^n ∂/∂x_n

and find the eigenvalue

2. Relevant equations

3. The attempt at a solution

Here's what I've done so far:

Differentiating with respect to t:

dF(tx)/dt = rt^(r-1)F(x)

But what do they mean by asking me to show it is an eigenfunction of the operator, and how would I go about calculating the eigenvalue? Any hints in the right direction would be super!

Thanks!

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# Homework Help: Differential geometry question

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