Okay there's a question I've been working on all day.
First it said: If v is an eigenvector of A with corresponding eigenvalue λ, show that v is an eigenvectors of A^-1. What is its corresponding eigenvalue?
The answer is 1/λ.
Then the second part of the question: Suppose a matrix A has real eigenvalues λ1 > λ2 > ..... > λn. Then was is lim k -> ∞A^kx0 for most initial vectors x0?
(The x0 is supposed to be "x knot" )
If anyone can help me with that second part I will appreciate it SO MUCH! Thanks