The eigen values of a symmetric matrix are all A. complex with non-zero positive imaginary part B. complex with non-zero negative imaginary part C. real D. pure imaginary

Option A is incorrect because the eigenvalues of a symmetric matrix are not necessarily complex. Option B is incorrect because the eigenvalues of a symmetric matrix are not necessarily complex with non-zero negative imaginary part. Option D is incorrect because the eigenvalues of a symmetric matrix are not necessarily pure imaginary.