Foundations of linear algebra
Vectors → Inner products → Linear maps → Matrices → Eigenvalues
- 01
Vectors
Axioms of a vector space; bases and coordinates.
about 7 min · 0 Interactive experiments · 2 Exercises
- 02
Inner products & Cauchy–Schwarz
Where length and angle come from; the whole inequality follows from “a projection is never longer”.
about 6 min · 0 Interactive experiments · 2 Exercises
- 03
Linear maps
Maps preserving addition and scaling, determined entirely by what they do to a basis.
about 7 min · 1 Interactive experiments · 2 Exercises
- 04
Matrices
Coordinate representation of linear maps; why matrix multiplication is defined the way it is.
about 8 min · 1 Interactive experiments · 2 Exercises
- 05
Eigenvalues
Directions along which a map is just a stretch.
about 8 min · 1 Interactive experiments · 2 Exercises
Position in the knowledge tree
Tap a concept to see what it builds on.
Foundations of calculus
Foundations of linear algebra
Introduction to differential equations
Planned