This series includes everything from Linear Algebra, including operations on one matrix, including solving linear systems, and Gauss-Jordan elimination, operations on two matrices, including matrix multiplication and elimination matrices, matrices as vectors, including linear combinations and span, linear independence, and subspaces, dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities, matrix-vector products, including the null and column spaces, and solving Ax=b, transformations, including linear transformations, projections, and composition of transformations, inverses, including invertible and singular matrices, and solving systems with inverse matrices, determinants, including upper and lower triangular matrices, and Cramer's rule, transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose, orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis, orthonormal bases and Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process, eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions.

Originally released by integral CALC, 2019. Streaming video file encoded with permission for digital streaming by Infobase on November 30, 2021.