Linear Algebra
Master the language of dimensions
8 topic modules. Practice problems with step-by-step solutions. Free to read. No account required.
Curriculum
8 chapters · from first principles to SVD and PCA
01
Systems of Linear Equations
Row reduction, Gaussian elimination, and solution types.
Read →02Vectors and Euclidean Spaces
Vector arithmetic, linear combinations, span, and independence.
Read →03Matrix Algebra
Matrix operations, inverses, and characterizations of invertibility.
Read →04Determinants
Cofactor expansion, properties, Cramer's rule, and geometric interpretation.
Read →05Vector Spaces
Subspaces, basis, dimension, rank, and the rank-nullity theorem.
Read →06Orthogonality and Least Squares
Orthogonal projections, Gram-Schmidt process, and least-squares fitting.
Read →07Eigenvalues and Eigenvectors
Characteristic equation, diagonalization, and complex eigenvalues.
Read →08Symmetric Matrices and Quadratic Forms
Spectral theorem, quadratic forms, SVD, and PCA.
Read →Start with Systems of Linear Equations
The starting point of linear algebra. Read at your own pace.