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).