Ebook: An introduction to linear algebra

Linear vector spaces -- Matrices -- Determinants -- Invertible matrices -- Linear systems -- Linear systems (cont'd) -- Factorization -- Linear dependence and independence -- Bases and dimension -- Coordinates and isomorphisms -- Rank of a matrix -- Linear mappings -- Matrix representation -- Inner products and orthogonality -- Linear functionals -- Eigenvalues and eigenvectors -- Normed linear spaces -- Diagonalization -- Singular value decomposition -- Differential and difference systems -- Least squares approximation -- Quadratic forms -- Positive definite matrices -- Moore-penrose inverse -- Special matrices.