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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  • All levels
  • 100 Lectures
  • 20h 17m
  • English
  • Lifetime access, certificate of completion (shareable on LinkedIn, Facebook, and Twitter), Q&A forum, subtitles in English
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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)

Lectures

  • 10 sections
  • 100 lectures
  • 20h 17m total length
Introduction and Outline
Preview
09:30
How to Succeed in this Course
08:45
Where to get the code
02:06
How to Take this Course
02:05
Lines and Planes
10:14
2 Equations and 2 Unknowns
12:58
3 Equations and 3 Unknowns
17:23
Gaussian Elimination
22:48
No Solutions
05:10
Infinitely Many Solutions
08:22
Review Summary
03:59
Suggestion Box
03:10
What is a Vector?
20:05
Adding and Subtracting Vectors
12:12
Dot Product
15:56
Dot Product (pt 2)
09:06
Dot Product Exercises in Python
17:49
Bonus Application: Neural Embeddings, Cosine Similarity (Optional)
21:36
Exercise: Normalizing a Vector
08:02
Exercise: The Vector Normal to a Plane
05:09
What is a Matrix?
27:59
Matrix Addition and Scalar Multiplication
03:52
Matrix Multiplication
18:02
Properties of Matrix Multiplication
08:19
Matrix-Vector Product
12:53
Application: Neural Networks
07:28
Element-Wise Product
03:23
Outer Product
09:50
Bonus Application: Replicating GPT-4
07:11
Matrix Exercises in Python
24:08
Linear Systems Revisited
06:19
Vectors and Matrices Summary
10:41
Identity Matrix
06:01
Diagonal Matrices
08:48
Matrix Inverse
24:20
Exercise: Inverse of the Inverse
07:59
Singular Matrices
08:14
Matrix Transpose
18:38
Properties of the Matrix Transpose
25:11
Symmetric Matrices
07:53
Transpose in Higher Dimensions
13:51
Orthogonal and Orthonormal Matrices and Vectors
14:27
Exercise: Orthogonal Matrices
03:21
Exercise: Inverse of a Product
02:25
Exercise: Transpose of Inverse of Symmetric Matrix
04:02
Exercise: Why Are Orthogonal Matrices Length- and Angle-Preserving?
09:26
Determinants (pt 1)
18:50
Determinants (pt 2)
23:09
Determinant Formula (Optional)
12:05
Determinant Identities (Optional)
06:01
Exercise: Determinant of a Unitary Matrix
02:23
Matrix Trace (Optional)
07:36
Positive Definite and Negative Definite Matrices
23:37
Exercise: Inverse of a Positive Definite Matrix
03:50
Exercise: Complete the Square
21:12
Matrix Operations Exercises in Python
13:56
Matrix Operations and Special Matrices Summary
11:35
Linear Independence and Dependence
34:31
Geometric Interpretation of Linear Combinations
07:46
The Rank of a Matrix
20:17
Matrix Decompositions (SVD, QR, LU, Cholesky)
24:50
Rank After Multplication
22:37
Low-Rank Approximations and Frobenius Norm
13:25
Applications: Recommender Systems and Topic Modeling (Optional)
17:09
Applications of SVD: Data Visualization and Feature Selection (Optional)
11:57
Bonus Application: LoRA for Diffusion Models and LLMs
09:14
Exercise: Generating a Positive Semi-Definite Matrix
05:15
Relationship Between Rank and Positive Definiteness
07:31
Matrix Decompositions in Python
20:09
Matrix Rank and Decompositions Summary
05:05
How to Find Eigenvalues and Eigenvectors (pt 1)
24:04
How to Find Eigenvalues and Eigenvectors (pt 2)
03:04
Exercise: Rotation Matrix
21:38
Exercise: Why Do A^TA and AA^T Have the Same Eigenvalues?
02:53
Exercise: Eigenvalues of the Inverse
02:48
Conjugate Transpose and Hermitian Matrices
11:31
Hermitian Matrices Have Real Eigenvalues
06:39
Diagonalization
24:11
Why Do Hermitian Matrices Have Orthogonal Eigenvectors?
06:29
Test for Positive Definiteness Using Eigenvalues
08:18
Determinant From Eigenvalues
03:02
Invertibility From Eigenvalues (Positive Definite Matrices Are Invertible)
04:54
Constructing the SVD ('Proof' of SVD)
26:00
Matrix Powers
08:30
Application: The Vanishing Gradient Problem
08:16
Functions of Matrices (Optional)
13:45
Eigenvalues in Python
25:16
Quiz: Square Root of a Matrix
05:50
Eigenvalues and Eigenvectors Summary
11:16
What is the Appendix?
03:47
Pre-Installation Check
04:13
Anaconda Environment Setup
20:21
How to install Numpy, Scipy, Matplotlib, Pandas, PyTorch, and TensorFlow
17:33
How to use Github & Extra Coding Tips (Optional)
11:12
Math Order for Machine Learning & Data Science
16:20
Can YouTube Teach Me Calculus? (Optional)
15:08
Is this for Beginners or Experts? Academic or Practical? Fast or slow-paced?
22:05
What order should I take your courses in? (part 1)
11:19
What order should I take your courses in? (part 2)
16:07
Where to get discount coupons and FREE deep learning material
05:49
PDF Notes

Reviews

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Testimonials and Success Stories

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H. Z.

Machine Learning Research Scientist
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United States

“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!”

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Wade J.

Data Scientist
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United States

“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.”

5.0
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Kris M.

Data Scientist
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United States

“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.”

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Steve M.

Machine Learning Research Scientist
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United States

“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.

Your courses are just what I have been seeking. I am a retired mathematician, statistician and Supply Chain executive from a large Fortune 500 company in Ohio. I also taught mathematics, statistics and operations research courses at a couple of universities in Northern Ohio.

I have taken many courses and have enjoyed the journey, I am not going to be critical of any of the organizations from whom I have taken courses. However, when I read a review about one of your courses in which the student was complaining that one would need a PhD in Mathematics to understand it, I knew this was the course (or series of courses) that I wanted. (Having advanced degrees in mathematics, I knew that it was highly unlikely that a PhD would actually be required.)”

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Saurabh W.

Data Scientist
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India

“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.”

5.0
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David P.

Financial Analyst
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United States

“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. :)”

5.0
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P. C.

Deep Learning Research Scientist
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China

“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.

Course by course, I was renewing the basics and the prerequisites. Thus, in several months, after every day studying under your guidance, I was able to gain enough intuitions and practical skills in order to begin progressing in my research. Having a solid background, it was just a pleasure to read all the relevant papers in the field as well as to make all the experiments needed for achieving my goal – creating a high-performance CNN for offline HCCR.

I believe, the professionalism of any teacher can be estimated by the feedback received from their students, and it’s of the utmost importance for me to thank you, Lazy Programmer!

I want you to know, in spite, that we have never actually met and you haven’t taught me privately, I consider you one of my greatest Teachers.

The most important things I have learned from you (some in the hard way, though) beside many exciting modern Deep Learning/AI techniques and algorithms are:

1) If one doesn’t know how to program something, one doesn’t understand it completely.

2) If one is not honest with oneself about one’s prior knowledge, one will never succeed in studying more advanced things.

3) Developing skills in BOTH Math and Programming is what makes one a good student of this major.

I am still studying your courses, and am certain I will ask you more than just a few technical questions regarding their content, but I already would like to say, that I will remember your contribution to my adventure in the Deep Learning field, and consider it as big as one of such great scientists’ as Andrew Ng, Geoffrey Hinton, and my supervisor.

Thank you, Lazy Programmer! 非常感谢您,Lazy 老师!

If you are interested, you can find my first paper’s preprint here:

https://arxiv.org/abs/xxx”

5.0
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Dima K.

Data Scientist
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Ukraine

“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.”

5.0
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Andres Lopez C.

Data Engineer
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United States

“This course is exactly what I was looking for. The instructor does an impressive job making students understand they need to work hard in order to learned. The examples are clear, and the explanations of the theory is very interesting.”

5.0
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Mohammed K.

Machine Learning Engineer
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Germany

“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.”

5.0
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Tom P.

Machine Learning Engineer
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United States

“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.”

5.0
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