Eigenvalue and eigenvector for a symmetric matrix 1. The problem statement, all variables and given/known data Let A be a n by n real matrix with the property that the transpose of A equals A. Show that if Ax = lambda x, for some non-zero vector x in C(n) then lambda is real, and the real part of x is an eigenvector of A. 2. Relevant equations 3. The attempt at a solution Since transpose of A equals A, A must be a symmetric matrix. But beyond that, I don't know where to start. Any help would be appreciated!