This course provides an introduction to linear algebra. Topics include: Gaussian elimination; matrix operations; matrix inverses; vector spaces and subspaces; linear independence and the basis of a space; row space and column space of a matrix; fundamental theorem of linear algebra; linear transformations; orthogonal vectors and subspaces; orthogonal bases; Gram-Schmidt method; orthogonal projections; linear regression; determinants: how to calculate them, properties, and applications; LineCalculating eigenvectors and eigenvalues, basic properties; matrix diagonalization; application to difference equations and differential equations; positive definite matrices; tests for positive definiteness; singular value decomposition; classification of states, transience and recurrence, classes of states; absorption, expected reward; stationary and limiting distributions.