Linear Algebra
Master the mathematics of vectors, matrices, and linear transformations through interactive visualizations
Syllabus
Vectors
The fundamental building block of linear algebra
Linear Combinations and Span
Combining vectors and understanding what they can reach
Matrices
The language of linear transformations
Linear Transformations
Functions that preserve vector structure
Matrix Multiplication
Composing transformations through matrices
The Determinant
Measuring how transformations scale space
Inverse Matrices
Reversing transformations and solving equations
Systems of Linear Equations
Finding where equations intersect
Rank and Null Space
What a matrix reaches and what it destroys
Dot Product
Projection and measuring similarity
Cross Product
Finding perpendicular vectors in 3D
Orthogonality and Projections
Perpendicular vectors and their remarkable properties
Change of Basis
Different coordinate systems for the same space
Eigenvectors and Eigenvalues
The axes that do not rotate under transformation
Diagonalization
The payoff of eigenvectors
Singular Value Decomposition
The universal matrix factorization
Least Squares
When there is no exact solution, find the best approximation