Math 0-1: Linear Algebra for Data Science & Machine Learning

A Casual Guide for Artificial Intelligence, Deep Learning, and Python Programmers

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Course Data

Lectures: 98
Length: 19h 57m
Skill Level: All Levels
Languages: English
Includes: Lifetime access, certificate of completion (shareable on LinkedIn, Facebook, and Twitter), Q&A forum

Course Description

Common scenario: You try to get into machine learning and data science, but there's SO MUCH MATH.

Either you never studied this math, or you studied it so long ago you've forgotten it all.

What do you do?

Well my friends, that is why I created this course.

Linear Algebra is one of the most important math prerequisites for machine learning. It's required to understand probability and statistics, which form the foundation of data science.

The "data" in data science is represented using matrices and vectors, which are the central objects of study in this course.

If you want to do machine learning beyond just copying library code from blogs and tutorials, you must know linear algebra.

In a normal STEM college program, linear algebra is split into multiple semester-long courses.

Luckily, I've refined these teachings into just the essentials, so that you can learn everything you need to know on the scale of hours instead of semesters.

This course will cover systems of linear equations, matrix operations (dot product, inverse, transpose, determinant, trace), low-rank approximations, positive-definiteness and negative-definiteness, and eigenvalues and eigenvectors. It will even include machine learning-focused material you wouldn't normally see in a regular college course, such as how these concepts apply to GPT-4, and fine-tuning modern neural networks like diffusion models (for generative AI art) and LLMs (Large Language Models) using LoRA. We will even demonstrate many of the concepts in this course using the Python programming language (don't worry, you don't need to know Python for this course). In other words, instead of the dry old college version of linear algebra, this course takes just the most practical and impactful topics, and provides you with skills directly applicable to machine learning and data science, so you can start applying them today.

Are you ready?

Let's go!

Suggested prerequisites:

  • Firm understanding of high school math (functions, algebra, trigonometry)

Testimonials and Success Stories

I am one of your students. Yesterday, I presented my paper at ICCV 2019. You have a significant part in this, so I want to sincerely thank you for your in-depth guidance to the puzzle of deep learning. Please keep making awesome courses that teach us!

I just watched your short video on “Predicting Stock Prices with LSTMs: One Mistake Everyone Makes.” Giggled with delight.

You probably already know this, but some of us really and truly appreciate you. BTW, I spent a reasonable amount of time making a learning roadmap based on your courses and have started the journey.

Looking forward to your new stuff.

Thank you for doing this! I wish everyone who call’s themselves a Data Scientist would take the time to do this either as a refresher or learn the material. I have had to work with so many people in prior roles that wanted to jump right into machine learning on my teams and didn’t even understand the first thing about the basics you have in here!!

I am signing up so that I have the easy refresh when needed and the see what you consider important, as well as to support your great work, thank you.

Thank you, I think you have opened my eyes. I was using API to implement Deep learning algorithms and each time I felt I was messing out on some things. So thank you very much.

I have been intending to send you an email expressing my gratitude for the work that you have done to create all of these data science courses in Machine Learning and Artificial Intelligence. I have been looking long and hard for courses that have mathematical rigor relative to the application of the ML & AI algorithms as opposed to just exhibit some 'canned routine' and then viola here is your neural network or logistical regression. ...


I have now taken a few classes from some well-known AI profs at Stanford (Andrew Ng, Christopher Manning, …) with an overall average mark in the mid-90s. Just so you know, you are as good as any of them. But I hope that you already know that.

I wish you a happy and safe holiday season. I am glad you chose to share your knowledge with the rest of us.

Hi Sir I am a student from India. I've been wanting to write a note to thank you for the courses that you've made because they have changed my career. I wanted to work in the field of data science but I was not having proper guidance but then I stumbled upon your "Logistic Regression" course in March and since then, there's been no looking back. I learned ANNs, CNNs, RNNs, Tensorflow, NLP and whatnot by going through your lectures. The knowledge that I gained enabled me to get a job as a Business Technology Analyst at one of my dream firms even in the midst of this pandemic. For that, I shall always be grateful to you. Please keep making more courses with the level of detail that you do in low-level libraries like Theano.

I just wanted to reach out and thank you for your most excellent course that I am nearing finishing.

And, I couldn't agree more with some of your "rants", and found myself nodding vigorously!

You are an excellent teacher, and a rare breed.

And, your courses are frankly, more digestible and teach a student far more than some of the top-tier courses from ivy leagues I have taken in the past.

(I plan to go through many more courses, one by one!)

I know you must be deluged with complaints in spite of the best content around That's just human nature.

Also, satisfied people rarely take the time to write, so I thought I will write in for a change. :)

Hello, Lazy Programmer!

In the process of completing my Master’s at Hunan University, China, I am writing this feedback to you in order to express my deep gratitude for all the knowledge and skills I have obtained studying your courses and following your recommendations.

The first course of yours I took was on Convolutional Neural Networks (“Deep Learning p.5”, as far as I remember). Answering one of my questions on the Q&A board, you suggested I should start from the beginning – the Linear and Logistic Regression courses. Despite that I assumed I had already known many basic things at that time, I overcame my “pride” and decided to start my journey in Deep Learning from scratch. ...


By the way, if you are interested to hear. I used the HMM classification, as it was in your course (95% of the script, I had little adjustments there), for the Customer-Care department in a big known fintech company. to predict who will call them, so they can call him before the rush hours, and improve the service. Instead of a poem, I Had a sequence of the last 24 hours' events that the customer had, like: "Loaded money", "Usage in the food service", "Entering the app", "Trying to change the password", etc... the label was called or didn't call. The outcome was great. They use it for their VIP customers. Our data science department and I got a lot of praise.



4 Lectures · 22min
  1. Introduction and Outline (09:30) (FREE preview available)
  2. How to Succeed in this Course (08:45)
  3. Where to get the code (01:42)
  4. How to Take this Course (02:05)

Linear Systems Review

8 Lectures · 01hr 24min
  1. Lines and Planes (10:14)
  2. 2 Equations and 2 Unknowns (12:58)
  3. 3 Equations and 3 Unknowns (17:23)
  4. Gaussian Elimination (22:48)
  5. No Solutions (05:10)
  6. Infinitely Many Solutions (08:22)
  7. Review Summary (03:59)
  8. Suggestion Box (03:10)

Vectors and Matrices

20 Lectures · 04hr 10min
  1. What is a Vector? (20:05)
  2. Adding and Subtracting Vectors (12:12)
  3. Dot Product (15:56)
  4. Dot Product (pt 2) (09:06)
  5. Dot Product Exercises in Python (17:49)
  6. Bonus Application: Neural Embeddings, Cosine Similarity (Optional) (21:36)
  7. Exercise: Normalizing a Vector (08:02)
  8. Exercise: The Vector Normal to a Plane (05:09)
  9. What is a Matrix? (27:59)
  10. Matrix Addition and Scalar Multiplication (03:52)
  11. Matrix Multiplication (18:02)
  12. Properties of Matrix Multiplication (08:19)
  13. Matrix-Vector Product (12:53)
  14. Application: Neural Networks (07:28)
  15. Element-Wise Product (03:23)
  16. Outer Product (09:50)
  17. Bonus Application: Replicating GPT-4 (07:11)
  18. Matrix Exercises in Python (24:08)
  19. Linear Systems Revisited (06:19)
  20. Vectors and Matrices Summary (10:41)

Matrix Operations and Special Matrices

25 Lectures · 04hr 58min
  1. Identity Matrix (06:01)
  2. Diagonal Matrices (08:48)
  3. Matrix Inverse (24:20)
  4. Exercise: Inverse of the Inverse (07:59)
  5. Singular Matrices (08:14)
  6. Matrix Transpose (18:38)
  7. Properties of the Matrix Transpose (25:11)
  8. Symmetric Matrices (07:53)
  9. Transpose in Higher Dimensions (13:51)
  10. Orthogonal and Orthonormal Matrices and Vectors (14:27)
  11. Exercise: Orthogonal Matrices (03:21)
  12. Exercise: Inverse of a Product (02:25)
  13. Exercise: Transpose of Inverse of Symmetric Matrix (04:02)
  14. Exercise: Why Are Orthogonal Matrices Length- and Angle-Preserving? (09:26)
  15. Determinants (pt 1) (18:50)
  16. Determinants (pt 2) (23:09)
  17. Determinant Formula (Optional) (12:05)
  18. Determinant Identities (Optional) (06:01)
  19. Exercise: Determinant of a Unitary Matrix (02:23)
  20. Matrix Trace (Optional) (07:36)
  21. Positive Definite and Negative Definite Matrices (23:37)
  22. Exercise: Inverse of a Positive Definite Matrix (03:50)
  23. Exercise: Complete the Square (21:12)
  24. Matrix Operations Exercises in Python (13:56)
  25. Matrix Operations and Special Matrices Summary (11:35)

Matrix Rank

12 Lectures · 03hr 12min
  1. Linear Independence and Dependence (34:31)
  2. Geometric Interpretation of Linear Combinations (07:46)
  3. The Rank of a Matrix (20:17)
  4. Matrix Decompositions (SVD, QR, LU, Cholesky) (24:50)
  5. Rank After Multplication (22:37)
  6. Low-Rank Approximations and Frobenius Norm (13:25)
  7. Applications: Recommender Systems and Topic Modeling (Optional) (17:09)
  8. Applications of SVD: Data Visualization and Feature Selection (Optional) (11:57)
  9. Bonus Application: LoRA for Diffusion Models and LLMs (09:14)
  10. Exercise: Generating a Positive Semi-Definite Matrix (05:15)
  11. Matrix Decompositions in Python (20:09)
  12. Matrix Rank and Decompositions Summary (05:05)

Eigenvalues and Eigenvectors

19 Lectures · 03hr 38min
  1. How to Find Eigenvalues and Eigenvectors (pt 1) (24:04)
  2. How to Find Eigenvalues and Eigenvectors (pt 2) (03:04)
  3. Exercise: Rotation Matrix (21:38)
  4. Exercise: Why Do A^TA and AA^T Have the Same Eigenvalues? (02:53)
  5. Exercise: Eigenvalues of the Inverse (02:48)
  6. Conjugate Transpose and Hermitian Matrices (11:31)
  7. Hermitian Matrices Have Real Eigenvalues (06:39)
  8. Why Do Hermitian Matrices Have Orthogonal Eigenvectors? (06:29)
  9. Test for Positive Definiteness Using Eigenvalues (08:18)
  10. Determinant From Eigenvalues (03:02)
  11. Invertibility From Eigenvalues (Positive Definite Matrices Are Invertible) (04:54)
  12. Diagonalization (24:11)
  13. Constructing the SVD ('Proof' of SVD) (26:00)
  14. Matrix Powers (08:30)
  15. Application: The Vanishing Gradient Problem (08:16)
  16. Functions of Matrices (Optional) (13:45)
  17. Eigenvalues in Python (25:16)
  18. Quiz: Square Root of a Matrix (05:50)
  19. Eigenvalues and Eigenvectors Summary (11:16)

Setting Up Your Environment (Appendix/FAQ by Student Request)

3 Lectures · 42min
  1. Pre-Installation Check (04:13)
  2. Anaconda Environment Setup (20:21)
  3. How to install Numpy, Scipy, Matplotlib, Pandas, IPython, Theano, and TensorFlow (17:33)

Effective Learning Strategies for Machine Learning (Appendix/FAQ by Student Request)

5 Lectures · 01hr 20min
  1. Math Order for Machine Learning & Data Science (16:20)
  2. Can YouTube Teach Me Calculus? (Optional) (15:08)
  3. Is this for Beginners or Experts? Academic or Practical? Fast or slow-paced? (22:05)
  4. What order should I take your courses in? (part 1) (11:19)
  5. What order should I take your courses in? (part 2) (16:07)

Appendix / FAQ Finale

2 Lectures · 08min
  1. What is the Appendix? (02:48)
  2. Where to get discount coupons and FREE deep learning material (05:49)


  • PDF Notes
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