Diagonalization

Symmetric and hermitian matrices, which arise in many applications, enjoy the property of always being diagonalizable. Also the set of eigenvectors of such matrices can always be chosen as orthonormal. The diagonalization procedure is essentially the same as outlined in Sec. 5.3, as we will see in our examples. Example 1 The horizontal motion of the system of masses and springs where all the masses are the same and the springs are the same, can be analyzed by diagonalizing the symmetric matrix