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?