Oxford Linear Algebra

Learn university-level linear algebra through a comprehensive video course covering the complete first-year undergraduate curriculum from the University of Oxford. Master fundamental concepts starting with elementary row operations and matrix inverses, then progress through determinant calculations using efficient methods. Explore eigenvalues and eigenvectors with detailed explanations and dive into the spectral theorem with complete proofs. Develop a deep understanding of vector spaces, including subspace identification, basis concepts, spanning sets, and linear independence. Study advanced topics such as the dimension formula for vector spaces, direct sums, and linear transformations. Apply the rank-nullity theorem and work with inner product spaces while learning the Gram-Schmidt process for orthogonalization. Each topic builds systematically on previous concepts, providing a thorough foundation in linear algebra suitable for mathematics, engineering, and science students.