Hi, I understand one of the motivations for eigenvalues/vectors is when you need to compute A^k * x. So we like to write, A = C*D*C^-1 and then A^k = C * D^k * C^-1, and D^k is trivial to compute. My professor said C^-1 and C can be though of as change of coordinate matrices. But from which basis? For example, C^-1 would take me from *some* basis to the basis of eigenvectors. But what is this *some* basis? Is it assumed that everything is coordinitized relative to some basis B in R^n. And then I want to change to the basis of eigenvectors B'?