Linear Algebra Tongji University 5th Edition Exercise 5, page 135, 20 questions, finally found that the basic solution system 1 and 3 need to be orthogonalized, why only unitized but not orthogonalized? Knowledge point: The eigenvectors of real symmetric matrices belonging to different eigenvalues are orthogonal.

So when dealing with orthogonal diagonalization, we only need to orthogonalize the eigenvectors of the eigenvalues of the real symmetric matrix A with multiplicity greater than 1.

And unity are necessary.