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Master linear algebra: theory and implementation in code (Udemy.com)

Learn concepts in linear algebra and matrix analysis, and implement them in MATLAB and Python.

Created by: Mike X Cohen

Last updated August 2026

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What you will learn

  • Understand theoretical concepts in linear algebra, including proofs
  • Implement linear algebra concepts in scientific programming languages (MATLAB, Python)
  • Apply linear algebra concepts to real datasets
  • Ace your linear algebra exam!
  • Apply linear algebra on computers with confidence
  • Gain additional insights into solving problems in linear algebra, including homeworks and applications
  • Be confident in learning advanced linear algebra topics
  • Understand some of the important maths underlying machine learning
  • The math underlying most of AI (artificial intelligence)

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Course Description

You need to learn linear algebra!

Linear algebra is perhaps the most important branch of mathematics for computational sciences, including machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and so on.

You need to know applied linear algebra, not just abstract linear algebra!

The way linear algebra is presented in 30-year-old textbooks is different from how professionals use linear algebra in computers to solve real-world applications in machine learning, data science, statistics, and signal processing. For example, the "determinant" of a matrix is important for linear algebra theory, but should you actually use the determinant in practical applications? The answer may surprise you, and it's in this course!

If you are interested in learning the mathematical concepts linear algebra and matrix analysis, but also want to apply those concepts to data analyses on computers (e.g., statistics or signal processing), then this course is for you! You'll see all the maths concepts implemented in MATLAB and in Python.

Unique aspects of this course

  • Clear and comprehensible explanations of concepts and theories in linear algebra.

  • Several distinct explanations of the same ideas, which is a proven technique for learning.

  • Visualization using graphs, numbers, and spaces that strengthens the geometric intuition of linear algebra.

  • Implementations in MATLAB and Python. Com'on, in the real world, you never solve math problems by hand! You need to know how to implement math in software!

  • Beginning to intermediate topics, including vectors, matrix multiplications, least-squares projections, eigendecomposition, and singular-value decomposition.

  • Strong focus on modern applications-oriented aspects of linear algebra and matrix analysis.

  • Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition.

  • Improve your coding skills! You do need to have a little bit of coding experience for this course (I do not teach elementary Python or MATLAB), but you will definitely improve your scientific and data analysis programming skills in this course. Everything is explained in MATLAB and in Python (mostly using numpy and matplotlib; also sympy and scipy and some other relevant toolboxes).

Benefits of learning linear algebra

  • Understand statistics including least-squares, regression, and multivariate analyses.

  • Improve mathematical simulations in engineering, computational biology, finance, and physics.

  • Understand data compression and dimension-reduction (PCA, SVD, eigendecomposition).

  • Understand the math underlying machine learning and linear classification algorithms.

  • Deeper knowledge of signal processing methods, particularly filtering and multivariate subspace methods.

  • Explore the link between linear algebra, matrices, and geometry.

  • Gain more experience implementing math and understanding machine-learning concepts in Python and MATLAB.

  • Linear algebra is a prerequisite of machine learning and artificial intelligence (A.I.).

Why I am qualified to teach this course:

I have been using linear algebra extensively in my research and teaching (in MATLAB and Python) for many years. I have written several textbooks about data analysis, programming, and statistics, that rely extensively on concepts in linear algebra. 

So what are you waiting for??

Watch the course introductory video and free sample videos to learn more about the contents of this course and about my teaching style. If you are unsure if this course is right for you and want to learn more, feel free to contact with me questions before you sign up.

I hope to see you soon in the course!

Mike


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Instructor Details

Mike X Cohen

I am a full-time educator and writer, and former professor of neuroscience. I "retired" from that position so I could focus my time and energy creating high-quality educational material just for you.

I have 20 years of experience teaching programming, data analysis, signal processing, statistics, linear algebra, and experiment design. I've taught undergraduate students, PhD candidates, postdoctoral researchers, and full professors. I have taught in "traditional" university courses, special week-long intensive courses, and Nobel prize-winning research labs. I have >100 hours of online lectures on neuroscience data analysis that you can find on my website and youtube channel. And I've written several technical books about these topics with a few more on the way.

I'm not trying to show off -- I'm trying to convince you that you've come to the right place to maximize your learning from an instructor who has spent two decades refining and perfecting his teaching style.

Over 350,000 students have watched over 50,000,000 minutes of my courses. Come find out why!

I have several free courses that you can enroll in. Try them out! You got nothing to lose ;)

                                                  -------------------------

By popular request, here are suggested course progressions for various educational goals:

MATLAB programming: Get Started with MATLAB; Master MATLAB; Image Processing

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Reviews

4.8

7,012 ratings on Udemy

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By Swayamjeet Bhagat on 6/8/2026

I was initially struggling to get the intuition of linear algebra for machine learning concepts and this course really helped me out to do so. Specially the visualisation and the foundation of linear algebra.

By Ankit Chimariya on 5/20/2026

I just completed this course, and it is easily one of the best linear algebra resources out there. Mike X Cohen has a fantastic teaching style that focuses heavily on geometric intuition rather than just boring, manual arithmetic. Learning how to implement these concepts directly in code (Python/MATLAB) completely changed how I view math. The sections on eigendecomposition and SVD were incredibly clear and gave me the exact foundation I need for machine learning and data science. The coding challenges were challenging but highly rewarding. Highly recommended for anyone who wants to actually understand linear algebra instead of just memorizing formulas!

By Udemy User on 5/1/2026

I already knew that Mike's books are clear and useful. To be honest, I thought his online classes might just be a recap of those books, and that would have been good value. In fact, the Udemy classes offer a whole new perspective. So I am delighted to be able to approach the topic from two angles. Mike's presentation (both written and spoken) is on par with the best university courses that I have taken. 5/5

By Omar Meqbel on 3/15/2026

I have started the course 3 months ago, and I'm still in section 11, I think that every part in the course is interesting, informative, conceptually clear, and relatable to other concepts/fields! Mainly, I registered because I wanted to deeply know/understand eigen-decomposition and SVD, and I noticed that almost every section builds up for this goal, and I'm super-duper excited to start sections 12, 13 and 14! Thank you Dr. Mike

By THOTA INDRA PAVAN THOTA INDRA PAVAN on 3/15/2026

good for learning linear algebra

By Yaheli Avni on 2/14/2026

Very clearly explains the core concepts necessary for a deep understannding of linalg. I love the simplicity of the slides, helps stay focused and is easy on the eyes.

By Ravi Kumar Javvaji on 2/4/2026

Wow! When I was in secondary school, I spent countless hours solving matrix problems without really understanding their real-world applications. This feels like a true aha moment for me now. Thank you very much.

By Severin Baschung on 11/28/2025

This course is a great way to start or extend ones current knowledge and the best I found so far when it comes to online learning. The explanations are clear and consice and the code challenges help to memorize and apply the concepts explained. However, for some parts towards the end (e.g. quadratic form) I wished there would be one or two real world application in the code challenges (e.g. where in a certain AI algorithm is concept X used). So to get most out of this course, I really recommend to find application yourself (ask your favourite LLM) and then try to code the algorithm from scratch.

By Claudio Pietronik on 11/4/2025

This is by far the best Linear Algebra course I’ve ever seen. Mike explains every concept with incredible clarity, breaking down even the most complex ideas into simple, intuitive steps. His teaching is hyper-detailed yet easy to follow. Truly a masterpiece for anyone who wants to really understand linear algebra.

By Mshtsudi on 10/20/2025

Since linear algebra is fundamental to machine learning, and the instructor’s teaching style in the ANTS courses appealed to me, I decided to enroll. Here are my thoughts: 1. The combination of theoretical knowledge and practical coding is highly effective and greatly enhances the understanding of core concepts. 2. The instructor successfully bridges the gap between linear algebra theory and its real-world applications. The examples provided are highly relevant to my research, particularly in time series analysis. 3. The video lengths are well-balanced, including both short and longer segments. The shorter videos are easy to complete and provide a sense of accomplishment, which motivates continued learning. 4. The course covers many key concepts in machine learning applications, and the content is very well-organized. Although I had studied linear algebra previously, I still found this course incredibly valuable.

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Overall Score : 96 / 100