This book is designed for an advanced course on linear algebra and covers the basics of the subject - from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity. It integrates MATLAB throughout the text. Each chapter includes a MATLAB subsection that discusses the various commands used to do the computations and offers codes for the graphics and algorithms used in the text. All material is presented from a matrix point of view. The treatment includes optional subsections covering applications. The final chapters move beyond basic matrix theory to discuss more advanced topics, such as decompositions, positive definite matrices, graphs, and topology.