Linear Algebra

Kristen Beck, Jan 24, 2025

Applets illustrating concepts from undergraduate linear algebra

Table of Contents

  1. Systems of Linear Equations
  2. Matrices
  3. The Determinant
    1. Determinant as Area
  4. Vector Spaces
    1. Example: Change of Basis
    2. Coordinate Vector Intuition
    3. Linear Combination of 2 Vectors in Space
    4. Vectors "in" a Plane
    5. Linear Combinations in the Plane
    6. Linear Operations in Space
  5. Inner Products
    1. Orthogonal Projection
  6. Linear Transformations
    1. Geometric Transformation Visualizer v1
    2. Geometric Transformation Visualizer v2
    3. Geometric Transformation Visualizer v3
  7. Eigenstuff
    1. Eigenvector Intuition

1.

Systems of Linear Equations


    This chapter does not contain any resources yet.

2.

Matrices


    This chapter does not contain any resources yet.

3.

The Determinant

  • 1. Determinant as Area

3.1.

Determinant as Area

– Kristen Beck

4.

Vector Spaces

  • 1. Example: Change of Basis
  • 2. Coordinate Vector Intuition
  • 3. Linear Combination of 2 Vectors in Space
  • 4. Vectors "in" a Plane
  • 5. Linear Combinations in the Plane
  • 6. Linear Operations in Space

4.1.

Example: Change of Basis

– Kristen Beck

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

5.

Inner Products

  • 1. Orthogonal Projection

5.1.

Orthogonal Projection

– Kristen Beck

6.

Linear Transformations

  • 1. Geometric Transformation Visualizer v1
  • 2. Geometric Transformation Visualizer v2
  • 3. Geometric Transformation Visualizer v3

6.1.

Geometric Transformation Visualizer v1

– Kristen Beck

6.2.

–

6.3.

–

7.

Eigenstuff

  • 1. Eigenvector Intuition

7.1.

Eigenvector Intuition

– Kristen Beck

Information