Essence of Linear Algebra (3Blue1Brown)

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

Course content

1 section · 16 lectures · 3h 0m

1. 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
   • 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