Essence of Linear Algebra: A Visual First Course

About this path

This learning path follows the popular Essence of linear algebra series by 3Blue1Brown. It covers the fundamental concepts of linear algebra, from vectors and matrices to eigenvalues and abstract vector spaces, using a visuals-first approach to build deep intuition. The path is organized into sections that group related videos, preserving the original order. Each video includes a summary and specific learning objectives to guide your study.

What you will learn

• Understand vectors, linear combinations, span, and basis vectors.
• Visualize linear transformations and how matrices represent them.
• Comprehend matrix multiplication as composition of transformations.
• Grasp the geometric meaning of the determinant and its computation.
• Solve linear systems using inverse matrices, column space, and null space.
• Interpret dot products and cross products geometrically and algebraically.
• Apply change of basis and understand eigenvectors and eigenvalues.
• Recognize the power of abstract vector spaces beyond geometric vectors.

Who this is for

Beginners who want a structured free introduction before deeper practice.

Curriculum