The Hitchhiker's Guide to Linear Algebra

Mathematics › Linear Algebra
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2 things in mathematics always had me in awe . One was complex number ( thanks to Welch Labs and this awesome book ) and other one was linear algebra ( thanks to the one and only great Grant Sanderson ) . From state of the art Machine Learning to the core of Quantum Computing , Linear Algebra is practically everywhere . In my level 2 in undergrad , I had to take Linear Algebra Course which was a course offered from the math department . To get some CS flavour and gain better intuition , I had to dive deep into other resources (details in the Resource section) . This is some kind of hybrid of personal note + blog of that time , contains some of the core stuffs that I had learnt and gained better intuition through this time . I have also implemented some of the basic LA algorithm stuffs in python for reference code along with the theories .

Hopefully this serves as a good starting point / refresher for anyone who is starting / practising ML / QC or anyone who is interested in general .

Contribution & Future Plan

This is yet to be completed . In Future , I have plans to add more applications like in ML and QC . If you are interested to contribute with anything (writeup/code/simulation) , feel free to send pull request / let me know .

Table of Content

➕ Introduction

➕ Row Reduction & Echelon Forms

🐍 Coding LA : Part 1 (Echelon & RREF)

➕ Vectors

➕ Ax = B and Ax = 0

➕ Linear Independence

➕ The Cool Stuff (Linear Transformations)

🐍 Coding LA : Part 2 (The Cool Stuffs in Application)

🐍 Coding LA : Part 3 (Homogeneous Coordinate)

➕ Matrix Operations

➕ Inverse of a Matrix

🐍 Coding LA : Part 4 (Inverse Matrix)

➕ Elementary Matrices

➕ Matrix Factorization

🐍 Coding LA : Part 5 (LU Decomposition)

➕ Determinant

➕ Vector Spaces

➕ Change of Basis

➕ Eigenvalue & Eigenvectors

Resources