Linear Algebra | Khan Academy

Khan Academy: Linear Algebra Course Curriculum

• Vectors: Covers linear dependence/independence, dot and cross products, Cauchy-Schwarz inequality, vector triangle inequality, and geometric applications (planes, distances, and normal vectors).
• Matrices and Systems: Focuses on solving systems via elimination, null space, column space, basis, rank, and nullity.
• Linear Transformations: Explores functions as transformations, matrix-vector products, image/preimage, kernel, and the properties of linear transformation operations.
• Inverses and Determinants: Discusses invertibility, surjective/injective functions, the solution set of $Ax=b$, and methods for finding inverses.
• Orthogonality: Covers orthogonal complements, projections onto subspaces, least squares approximation, and orthonormal bases.
• Gram-Schmidt Process: Details the algorithm for constructing orthonormal bases and the properties of orthogonal matrices (preserving angles and lengths).
• Eigen-everything: Introduces eigenvalues and eigenvectors, including calculations for 2x2 and 3x3 matrices, eigenspaces, and the utility of eigenbases for coordinate systems.