Advanced Linear Algebra

This is linear algebra as rigorous and beautiful as it can be. The development of the presented concepts is in terms of advanced abstract algebra; particularly rings and modules. However, no prior knowledge of abstract algebra is required to study the book, and this is the very element that makes it a masterpiece. Readers unfamiliar though with basic abstract algebra should expect to progress quite slowly throughout the book, given that they show devotion and enough faith to let their minds be guided by the author's educating pen. Diligent study of the book leads to beautiful insights being emerged that are far from trivial. For this reason, it is highly recommended that the prospective reader possesses a good level of mathematical maturity and is already familiar to a sufficient degree with linear algebra and matrix analysis, e.g. at the level of C. Meyer's "Matrix Analysis and Applied Linear Algebra", which is an excellent first study of the topic. "Advanced Linear Algebra" is a book that addresses those who love linear algebra (or algebra) and are serious about mastering the pertaining concepts. The book is invaluable for combining rigor, depth of exposition, excellent notation and educational character for a topic of immense importance that pervades almost every aspect of modern quantitative sciences.