🚀 go-pugleaf

I have linear system of equations

Ax=y

and A is 10000x10000 and full (it is Toeplitz matrix). 
The conjugate gradient method I use converges in 50 iterations 
for known y. This means, I guess, that the eigenvalues are clustering ?

a) Is there a way to form an INVERSE of A from
a very limited amount of eigenvalues and eigenvectors ?
Spectral theorem ?

b) Can I get these eigenpairs from the conjugate gradient 
method ? 

c) Can I expect that 50 eigenvectors is enough to 
represent the inverse ?

Answers: "Why do you need inverse ?", "Never, ever use 
inverse when dealing with linear algebra"  do not count as correct.

Cheers, 
Peter