Linear Algebra
Coursera
University of Sydney course covering geometric vectors, dot and cross products, systems of equations solved by Gaussian elimination, matrix arithmetic, determinants, eigenvalues and diagonalisation. Finishes with linear transformations and Markov processes, emphasising geometric intuition over formal proof.
More resources on Linear Algebra
Immersive Linear Algebra
Interactive linear algebra textbook with dynamic visualizations covering vectors, matrices, transformations, eigenvalues, and decompositions.
Linear Algebra Done Right
Rigorous linear algebra text emphasizing vector spaces, linear maps, and abstract structure over computational techniques and determinants.
3Blue1Brown
Visual mathematics explanations using animations to build deep intuition for linear algebra, calculus, differential equations, and mathematical concepts.
Applied Linear Algebra (Boyd & Vandenberghe)
Modern linear algebra presented as the essential infrastructure for data science and AI optimization.
A Vision of Linear Algebra (MIT RES.18-010)
Ten short lecture videos with slides presenting a recommended order for linear algebra: column space, the four fundamental subspaces, orthogonality, eigenvalues, singular values, least squares, and five matrix factorizations including A = CR. Gives a big-picture review connecting the core ideas.
Khan Academy Linear Algebra: Vectors and Spaces
Khan Academy's first linear algebra unit: short videos and exercises on vectors, linear combinations, span, linear independence, subspaces and bases, dot and cross products, solving systems by row reduction, and null and column spaces, building the foundation for matrix transformations.