Comment by zkmon
Comment by zkmon 9 hours ago
There are a lot more ways to look at and understand these mysterious beasts called matrices. They seem to represent a more fundamental primordial truth. I'm not sure what it is. Determinant of a matrix indicate the area of or volume spanned by its component vectors. Complex matrices used in Fourier transform are beautiful. Quantum mechanics and AI seem to be built on matrices. There is hardly any area of mathematics that doesn't utilize matrices as tools. What exactly is a matrix? Just a grid of numbers? don't think so.
The fundamental truth is that matrices represent linear transformations, and all of linear algebra is developed in terms of linear transformations rather than just grid of numbers. It all becomes much clearer when you let go of the tabular representation and study the original intentions that motivated the operations you do on matrices.
My appreciation for the subject grew considerably after working through the book "Linear Algebra done right" by Axler https://linear.axler.net