[Linear Algebra]
1a) Let A be an n × n-matrix. Suppose that A has n eigenvectors linearly independent. v1, ..., vn associated with n eigenvalues λ1, ..., λn. If we denote by S the matrix whose column i is vi, and by D the diagonal matrix of eigenvalues, show that AS = SD. Hint: Express in matrix the equations Avi = viλi).
1b) Use the previous item to prove that if A has n eigenvectors linearly independent, then it is diagonalizable.