# Eigenvalue vs Variance

I recently read that eigenvalue indicates the variance for an attribute/dimension. But is there a relation/equation between eigenvalue and variance? Is is right to say eigenvalue is equal to variance (but the direction can be different)?

I tried a simple example in R:

x= matrix(c(-1,2,2,2,2,-1,2,-1,2), 3, 3)
var (x)
eigen(x)


Variance was 3, 3, 3, eigenvalue was 3, 3, -3.

Can someone please explain me the relationship?