Science & research

Essence of Linear Algebra (3Blue1Brown)

Free

16 video lectures (3h 0m)
Certificate of completion
Ask the teacher your doubts
Watch on the web and in the Android app
Learn more

About this course

See linear algebra instead of only computing it. Grant Sanderson of 3Blue1Brown builds the geometric intuition behind vectors, matrices, determinants and eigenvectors with beautiful animations, the understanding most textbooks skip. Who it's for: Class 12 and college students, engineering students, and anyone heading into machine learning, computer graphics or physics. These are the free, official videos of the "Essence of linear algebra" series from the 3Blue1Brown YouTube channel (youtube.com/@3blue1brown). All videos belong to 3Blue1Brown; Sikhami is not affiliated with 3Blue1Brown and simply arranges the public playlist into a course, so you can learn one lesson at a time and keep track of your progress.

What you will learn

• Vectors, linear combinations, span and basis vectors • Linear transformations and what a matrix really is • Matrix multiplication as composition, and 3D transformations • The determinant, inverse matrices, column space and null space • Dot products, cross products and duality • Cramer's rule, explained geometrically • Change of basis, eigenvectors and eigenvalues, and abstract vector spaces

This course at a glance

Lectures: 16 video lectures
Video: 3h 0m in all
Level: Class 12, Undergraduate
Language: English
Access: Lifetime access
Certificate: On completion

Lectures last updated September 2026

Course content

1 section · 16 lectures · 3h 0m

1. Essence of linear algebra
- Vectors | Chapter 1, Essence of linear algebra9m
- Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra9m
- Linear transformations and matrices | Chapter 3, Essence of linear algebra10m
- Matrix multiplication as composition | Chapter 4, Essence of linear algebra10m
- Three-dimensional linear transformations | Chapter 5, Essence of linear algebra4m
- The determinant | Chapter 6, Essence of linear algebra10m
- Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra12m
- Nonsquare matrices as transformations between dimensions | Chapter 8, Essence of linear algebra4m
- Dot products and duality | Chapter 9, Essence of linear algebra14m
- Cross products | Chapter 10, Essence of linear algebra8m
Show all 16 lectures
- Cross products in the light of linear transformations | Chapter 11, Essence of linear algebra13m
- Cramer's rule, explained geometrically | Chapter 12, Essence of linear algebra12m
- Change of basis | Chapter 13, Essence of linear algebra12m
- Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra17m
- A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebra13m
- Abstract vector spaces | Chapter 16, Essence of linear algebra16m

How long it takes

3h 0m of video in 16 lectures. Pick a pace that suits you:

Steady
7 days
at 30 minutes a day
Regular
4 days
at 1 hour a day
Fast track
2 days
at 2 hours a day

Video time only: practice takes a little longer. Your place in every lecture is saved, so you can stop any time.

Earn a certificateLearn more

Watch every lecture, then claim a certificate of completion with your name on it.

Its own web page and code, so a school or an employer can check it is real
Save it as a PDF or print it
Included with the course, at no extra cost

Who teaches it

Sikhami InstituteNew Delhi · 297 courses · 693 learners · 472 followersSikhami Institute is Sikhami's own institute for free learning. We pick some of the best free courses on YouTube, from Harvard's CS50, MIT, NPTEL, Khan Academy, Google, Microsoft, the BBC, Crash Course, PW, Magnet Brains, CodeWithHarry and many more, and turn them into proper courses on Sikhami that you can follow lesson by lesson while your progress is saved. Free courses in every category, in English and Hindi: school and competitive exams, programming and AI, languages, music and dance, art, yoga and fitness, cooking, trades, business, marketing, farming and more. All videos belong to their creators and play from their official YouTube channels, and each course credits its creator. Questions or suggestions? Write to help@sikhami.com.

Questions people ask

Is this course free?

Yes. Joining is free, and the lectures unlock as soon as you join. Once you join, it is yours for life.

How long is the course?

16 video lectures, 3h 0m of video in all. At an hour a day, the videos take 4 days. You learn at your own pace; there are no fixed class times.

Do I get a certificate?

Yes. When you have watched every lecture, you can claim a certificate of completion. It has its own page and code, so anyone can check that it is real. About certificates

What language is it taught in?

English.

Can I learn on my phone?

Yes. Watch on the website or in the Sikhami app for Android with the same account. Your place in every lecture is saved, so you can switch between them.

Can I ask the teacher a doubt?

Yes. Ask it in the questions on the course page, or from inside any lecture while you watch. You can also keep your own notes on each lecture.

Who made these videos?

The lectures are the free, public videos of the YouTube playlist "Essence of linear algebra", and they belong to their creator. Sikhami arranges them into a course, so you can learn one lecture at a time and keep track of your progress.

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