I am reading through a proof and one line of it is not immediately obvious to me, despite it's simplicity. It relates to eigenvalues of a (nearly) full rank, symmetric matrix. Say we have a symmetric matrix A(nxn) that has rank=n-1. Why is this enough to say that all eigenvalues of A are distinct? Note that the symmetry is important for the result to hold, but I don't understand why. Thank you in advance.