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Home/Linear Algebra

Linear Algebra Learning Hub

Master linear algebra through comprehensive courses and extensive practice problems

12 Comprehensive Courses140+ Hours ContentAlways Free

Foundations & Vector Spaces

Essential prerequisites: algebraic structures (groups, fields), complex numbers, equivalence relations, Gaussian elimination, and vector space definition

Foundation10-12 hours

Algebraic Structures

Complex Numbers

Equivalence Relations

Subspaces & Linear Independence

Subspaces, linear span, linear dependence and independence, and the Steinitz exchange lemma

Linear Independence

Basis & Dimension, Direct Sums & Quotients

Basis, dimension, coordinate systems, direct sums, and quotient spaces

Core10-12 hours

Linear Maps & Kernel/Image

Linear maps, their kernel (null space) and image (range), and characterizations of injectivity and surjectivity

Core10-12 hours

Rank-Nullity & Isomorphisms

The fundamental Rank-Nullity Theorem and the concept of isomorphisms between vector spaces

Advanced Core8-10 hours

Rank-Nullity Theorem

Dimension Invariant

Matrix representation of linear maps, matrix operations, and special matrices

Core12-15 hours

Matrix Representation

Matrix Operations

Special Matrices

Matrix Inverses, Elementary Matrices & Dual Spaces

Matrix inverses, elementary matrices, matrix rank, and dual spaces

Advanced Core12-15 hours

Matrix Inverses

Elementary Matrices

Determinant definition, properties, computation methods, Laplace expansion, and adjugate matrices

Core12-15 hours

Determinant Definition

Eigenvalues & Eigenvectors

Eigenvalue theory, characteristic polynomials, diagonalization, Jordan form, and Cayley-Hamilton theorem

Advanced15-18 hours

Characteristic Polynomial

Diagonalization

Inner Product Spaces

Inner products, orthogonality, Gram-Schmidt process, orthogonal projections, and spectral theorem

Advanced15-18 hours

Advanced Topics Part 1

Singular Value Decomposition (SVD) and quadratic forms with applications

Advanced12-15 hours

Low-Rank Approximation

Quadratic Forms

Advanced Topics Part 2

Multilinear algebra, tensors, and real-world applications in ML, graphics, quantum computing, and more

Advanced12-15 hours

Multilinear Algebra

Machine Learning