š Linear Algebra
Based on Jim Hefferon's Linear Algebra, licensed GFDL + CC BY-SA 2.5.
Five chapters from systems of equations to eigenvalues. Runnable Python, SVG diagrams, plain English.
| Chapter | |||
|---|---|---|---|
| 1. | Linear Systems | Row reduction turns any system of equations into echelon form, making solutions obvious | š |
| 2. | Vector Spaces | Subspaces, linear independence, basis, and dimension ā the vocabulary for everything that follows | š |
| 3. | Maps Between Spaces | Homomorphisms are structure-preserving maps, and every one of them is a matrix in disguise | š |
| 4. | Determinants | A single number that tells you whether a matrix is invertible and how it scales volume | š |
| 5. | Similarity | Eigenvalues, eigenvectors, and Jordan form ā choosing the basis that makes a map simplest | š |
šŗ Video lectures: 3Blue1Brown: Essence of Linear Algebra
Neighbors
- š¤ Machine Learning — linear regression, PCA, and neural networks are linear algebra in disguise
- ā« Calculus — multivariable calculus runs on vectors and matrices
- š Abstract Algebra — vector spaces are modules over a field
- ā³ Geometry — transformations and dot products connect
- š Control Theory — state space representation is matrix algebra