Basic linear algebra

This textbook has grown up in the last twenty years, based on my courses of Algebra taught for first year students in Computer Science at the “Babe¸s-Bolyai” University of Cluj-Napoca. Besides the rather classical mathematical content, we also present some illustrations of the interplay between Algebra and Computer Science, which offers bidirectional applications. If we only restrict to Linear Algebra for Computer Science, then we should mention applications to several important research topics in Computer Science, such as Networks, Theory of Computation, Mathematics of Computing, Information Systems, Security and Privacy, Computing Methodologies and Applied Computing (see the corresponding addendum for some further details). The material is directed towards first year students in Computer Science, but it may be useful to anyone interested in an introduction to Linear Algebra and its applications to Computer Science.