0.1 Final Thoughts

I wanted to include my final thoughts on these notes and notice on some topics that were not covered here, and I guess I can use the help of appendix.

First, as mentioned in the prefix, these are the notes that I took while learning the essence of linear algebra in 8 weeks. That being said, while most of the fundamental concepts were covered, other topics like dual space, cross product, euclidean inner product, and more advanced concepts including Markov chains and Jordan canonical forms are not included here. After the initial release, I will continue to update these notes for the second edition as I will likely take linear algebra course again in college as a student who will major in pure math. In the meantime, I highly recommend watching 3Blue1Brown series on linear algebra as it really helped me visually understand different concepts and formulas.

As I also study different concepts in machine learning, I realized how important linear algebra is outside “mathematics.” Literally, vectors are used everywhere including, but not limited to encoding/decoding and backpropagation. One of the reasons why I find math so fascinating is due to duality and applications that just seems so perfect. Matrices can be interpreted with heavy computation while it can also be interpreted geometrically with change in area. The two seemingly unrelated topics actually imply the same exact concept. Similarly, what else can we use instead of matrix multiplication and addition for forward pass in machine learning? The way it seems so intuitive and “perfect” is I think one of the most beautiful side of mathematics. Really, if you completed these notes, I highly recommend learning math behind machine learning if you like finding different applications of mathematics. More information can be found in the next part of LibreNotebook.