Linear Algebra
All modules
Read the lesson, follow the worked examples, then practice.
Chapter 01
Systems of Linear Equations
Row reduction, Gaussian elimination, and solution types.
75 min
Chapter 02
Vectors and Euclidean Spaces
Vector arithmetic, linear combinations, span, and independence.
60 min
Chapter 03
Matrix Algebra
Matrix operations, inverses, and characterizations of invertibility.
75 min
Chapter 04
Determinants
Cofactor expansion, properties, Cramer's rule, and geometric interpretation.
60 min
Chapter 05
Vector Spaces
Subspaces, basis, dimension, rank, and the rank-nullity theorem.
90 min
Chapter 06
Orthogonality and Least Squares
Orthogonal projections, Gram-Schmidt process, and least-squares fitting.
90 min
Chapter 07
Eigenvalues and Eigenvectors
Characteristic equation, diagonalization, and complex eigenvalues.
90 min
Chapter 08
Symmetric Matrices and Quadratic Forms
Spectral theorem, quadratic forms, SVD, and PCA.
90 min