Concepts you described can't happen without a Step 1 in even approaching linear algebra. These types of explanations help many take that first step.
Right, my exact sentiment.
Thinking of matrices as spreadsheets is barely abstraction. Seeing the derivative operator represented as a matrix, acting over the polynomial vector space can open your eyes.
Taking the determinant of that matrix shows that d/dx isn't invertible.
Thinking of the fixed point of the transformation yields exp, the eigenfunction of the operator.
https://blog.classycode.com/implementing-a-cpu-in-vhdl-part-...