1. The problem statement, all variables and given/known data Consider a symmetric (and hence diagonalizable) n x n matrix A. The eigenvectors of A are all linearly independant, and hence they span the eigenspace Rn. Since the matrix A is symmetric, there exists an orthonormal basis consisting of eigenvectors. My questions are: 1) Will this orthonormal basis of eigenvectors also span the same space Rn? 2) If two vectors are linearly independant, will they also be orthogornal?