R is a programming language and environment for statistical and graphical analysis. It is a free software project, the result of the GNU implementation of the classic scientific language S-Plus. Different libraries or packages can be loaded for specific calculus, algebra, statistics, or graphics purposes. R is available for Windows, Macintosh, Unix, and GNU / Linux operating systems. This book delves into the topics of Linear Algebra and its treatment with R. Among other topics, matrix algebra is addressed in the real and complex fields, diagonalization, eigenvalues and eigenvectors, vector spaces, linear applications, quadratic forms, equations and systems, representation of surfaces and representation of curves in explicit, implicit and polar coordinates