This book provides a compact but thorough introduction to the topic. This book is intended for a senior undergraduate and for a beginning graduate one-semester course. The subject matter has been organized in the form of theorems and their proofs, and the presentation is rather unconventional.

Linear Vector Spaces. Matrices. Determinants. Invertible Matrices. Linear Systems. LU Factorization. Linear Dependence and Independence. Bases and Dimension. Coordinates and Isomorphisms. Rank of a Matrix. Linear Mappings. Matrix Representation of Linear Mappings. 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.

Ravi P. Agarwal is a professor and the chair of the Department of Mathematics at Texas A&M University-Kingsville. Dr. Agarwal is the author or co-author of 1400 scientific papers and 40 monographs. His research interests include nonlinear analysis, differential and difference equations, fixed point theory, and general inequalities.

Cristina Flaut is a professor in the Department of Mathematics and Computer Science at Ovidius University, Romania. Dr Flaut is the co-author of more than two dozen papers and monographs. Her research interests include linear algebra, non-associative algebras, coding theory.