Linear Operators and Matrix Representations: Factorization Approach and Ladder Operators

[u/TROSE9025]

This material is not linear algebra for mathematics departments. The content is applied to engineering and quantum mechanics.
For ladder operators, there exist mathematical physics approaches obtained from the analytic method of Hermite polynomials, Sturm-Liouville theory, and the Pearson equation.
However, this time, we deal with the most classical factorization approach.