"What are the conditions for diagonalization of N-order matrices?" Theorem 4 in the previous section gives a necessary and sufficient condition, but this necessary and sufficient condition is the simplest one. In fact, there are many other conditions (that is, "general discussion" mentioned later), which are much more complicated than this condition, so the textbook thinks it is more complicated.

Next, the problem is limited to a small range of symmetric matrices (in fact, Tongji University linear algebra refers to a symmetric matrix in the range of real numbers). From this, the fourth section "Diagonalization of Symmetric Matrix" is expanded.

"What are the conditions for diagonalization of N-order matrices?" It is not discussed in the course of linear algebra for non-mathematics majors, but it is generally discussed in mathematics majors. If you want to know, you can refer to some popular math textbooks:

Peking University, Third or Fourth Edition of Advanced Algebra.

Qiu advanced algebra

Fudan University Yao Musheng Advanced Algebra Third Edition.

Zhang Xianke's Advanced Algebra

For example, section 5.6 of Qiu's Advanced Algebra corresponds to "What conditions must an N-order matrix have to be diagonalized?" Section 5.7 studies the diagonalization of the corresponding real symmetric matrix (that is, the fourth section of Chapter 5 of Tongji).