[SOLVED] Eigenvectors and their inverses 1. The problem statement, all variables and given/known data After submitting the first question, I thought of a new one - so there are two questions: 1) I have a n x n matrix A and it has n (not necessarily different) eigenvalues. I can write the matrix A as the product of: S*D*S^(-1), where D is the diagonalmatrix which has the eigenvalues as it's entries. S contains the eigenvalues (in the same order as they are written in D) and S^-1 is the inverse of S. Some places I see they write it as S^(-1)*D*S, and some places as S*D*S^(-1). Is it always the matrix to the left of D that contains the eigenvectors? 2) If I have a matrix A that represents a transformation L from R^4 -> R given by [1 -1 3 0], then how can I determine if L is linear from A? Thanks in advance, sincerely Niles.