3Blue1Brown: Essence of Linear Algebra
Grant Sanderson
  • Course duration: 2h 34m
    14 exercises
In this liveVideo course mathematician Grant Sanderson—better known on YouTube as 3blue1brown—lays out the foundations of linear algebra in his distinctive animation-and-visuals style. FREE ON LIVEVIDEO, Essence of Linear Algebra emparts an understanding of algebra that extends beyond the numbers into how and why algebra is so essential to the real world. Intuitive visualizations, fun storytelling, and quirky animation teach linear algebra like you never learned it in math class!

About the subject

Linear algebra deals with linear transformations over vectors, making it a central aspect of almost all mathematics fields. It’s vitally important for scientific computing and data analysis in order to model phenomena and make accurate predictions.

About the video

Essence of Linear Algebra untangles a complex-but-vital mathematical topic. It uses the unique visualizations-first approach of creator Grant Sanderson to demonstrate what linear algebra is, how it works, and why it is so important to the real world. You’ll learn how to think about vectors in context, understanding how linear transformation works and its relation to matrices, about 3D linear transformations, and more. This liveVideo course is ABSOLUTELY FREE. Just add it to the cart for $0.00 and check out.
Table of Contents detailed table of contents

Essence of linear algebra

Vectors, what even are they?

Linear combinations, span, and basis vectors

Linear transformations and matrices

Matrix multiplication as composition

Three-dimensional linear transformations

The determinant

Inverse matrices, column space and null space

Nonsquare matrices as transformations between dimensions

Dot products and duality

Cross products

Cross products in the light of linear transformations

Change of basis

Eigenvectors and eigenvalues

Abstract vector spaces

Additional resources

Manning titles


You’ll need basic math skills.

What you will learn

  • How physicists, computer scientists, and mathematicians think about vectors
  • Vector concepts of span, linear combinations, linear dependence, and bases
  • The determinant of a linear transformation
  • Dot products and duality
  • Geometrically explaining Cramer’s rule
  • Eigenvectors and eigenvalues

About the instructor

Grant Sanderson studied mathematics at Stanford, with a healthy bit of computer science along the way. His YouTube channel 3blue1brown presents math with a visuals-first approach and has over 2.2 million subscribers.

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