Updated on Aug 2024

Lectures of Linear Algebra

These lecture notes are intended for introductory linear algebra courses, suitable for university students, programmers, data analysts, algorithmic traders and etc.

The lectures notes are loosely based on several textbooks:

1. Linear Algebra and Its Applications by Gilbert Strang
2. Linear Algebra and Its Applications by David Lay
3. Introduction to Linear Algebra With Applications by DeFranza & Gagliardi
4. Linear Algebra With Applications by Gareth Williams

However, the crux of the course is not about proving theorems, but to demonstrate the practices and visualization of the concepts. Thus we will not engage in precise deduction or notation, rather we aim to clarify the elusive concepts and thanks to Python/MATLAB, the task is much easier now.

Prerequisites

Though the lectures are for beginners, it is beneficial that attendants had certain amount of exposure to linear algebra and calculus.

And also the attendee are expected to have basic knowledge (3 days training would be enough) of

• Python
• NumPy
• Matplotlib
• SymPy

All the codes are written in an intuitive manner rather than efficient or professional coding style, therefore the codes are exceedingly straightforward, I presume barely anyone would have difficulty in understanding the codes.

Environment Setup

I use poetry to management environment, if you happen to use VS code like me, please follow the steps below:

1. In Windows powershell and install poetry (Invoke-WebRequest -Uri https://install.python-poetry.org -UseBasicParsing).Content | python -p
2. Navigate to cd $env:APPDATA\Python\Scripts, check if poetry being installed.
3. Open a notepad notepad $profile and set alias for poetry Set-Alias poetry "C:\Users\user\AppData\Roaming\Python\Scripts\poetry.exe" in notepad, I prefered this way, because sometimes setting env path not working in windows.
4. Reload profile by . $profile.
5. If you are on your personal computer Set-ExecutionPolicy RemoteSigned -Scope CurrentUser to unstrict your execution policy and choose Y.
6. Resume the default restricted policy for security Set-ExecutionPolicy Restricted -Scope CurrentUser.
7. Now check poetry --version, if you see the version printed, good to go.
8. You choose to use poetry update, or just manage version at your own convenience.

What to Expect from Notes

These notes will equip you with most needed and basic knowledge for other subjects, such as Data Science, Econometrics, Mathematical Statistics, Financial Engineering, Control Theory and etc., which heavily rely on linear algebra. Please go through the tutorial patiently, you will certainly have a better grasp of the fundamental concepts of linear algebera. Then further step is to study the special matrices and their application with your domain knowledge.

Contents

Please access my webiste for better reading experience: Linear Algebra for Python
Chapter 1 - Linear Equation System
Chapter 2 - Basic Matrix Algebra
Chapter 3 - Determinant
Chapter 4 - LU Factorization
Chapter 5 - Vector Addition, Subtraction and Scalar Multiplication
Chapter 6 - Linear Combination
Chapter 7 - Linear Independence
Chapter 8 - Vector Space and Subspace
Chapter 9 - Basis and Dimension
Chapter 10 -Null Space vs Col Space, Row Space and Rank
Chapter 11 - Linear Transformation
Chapter 12 - Eigenvalues and Eigenvectors
Chapter 13b - Principal Component Analysis
Chapter 13a - Diagonalization
Chapter 14 - Applications to Dynamic System
Chapter 15 - Innear Product and Orthogonality
Chapter 16 - Gram-Schmidt Process and QR Decomposition
Chapter 17 - Symmetric Matrices , Quadratic Form and Cholesky Decomposition
Chapter 18 - The Singular Value Decomposition
Chapter 19 - Multivariate Normal Distribution

Screen Shots Examples