Essential Linear Algebra with Applications

Titu Andreescu is an Associate Professor of Mathematics at the University of Texas at Dallas.

• Preface.- Linear Phenomena and Euclidean Spaces of Small Dimension.- Concrete Vector Spaces.- Vector Spaces and Subspaces.- Linear Transformations.- More Matrix Algebra and Determinants.- General Theory of Linear Equations.- Eigenvectors.- Orthogonality.- Forms.- Vector Spaces over Finite Fields.- Appendix A: Complex Numbers.- Appendix B: Polynomials over Complex Numbers.- References.- Index.

"This book gives a rigorous introduction to linear algebra from a mathematical point of view. ... The book presents a 'problem-based' approach, i.e., the author gives the precise theory to permit the reader to solve many different problems. ... The book contains many well-chosen examples and exercises. Also, many problems are completely solved." (Julio Benitez, Mathematical Reviews, June, 2015) "The present book, as its title indicates, introduces the essential concepts of linear algebra and considers some of its applications. ... the book is very suitable for students who are going to prepare for competitions and Olympiads. Moreover, the solved problems make it a very good problem book, with nice ideas, for anybody working with linear algebra. I recommend this book for students, and also for classroom use by teachers." (Mehdi Hassani, MAA Reviews, April, 2015) "The present book is a wellcomed addition at the present literature. The approach is elementray, however still rigorous and detailed. It covers the standard topics on linear algebra taught in a two-semester course, from elementray matrix theory to canonical forms and bilinear forms. ... I would be happy to teach linear algebra from this book and ask students to work on problems from it." (A. Arvanitoyeorgos, zbMATH 1309.15001, 2015)