Linear Algebra Paperback

Belkacem Said-Houari

This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing the necessary concepts of eigenvalues and eigenvectors, as well as the theory of symmetric and orthogonal matrices. Each idea presented is followed by examples.

3319637924

9783319637921

English

Birkhauser

25 Oct 2017

384

Belkacem Said-Houari is Professor at the Mathematics Department, University of Sharjah, Sharjah and author of the book on Differential Equation (ISBN 978-3-319-25734-1) in the same series.

This book can be used as a textbook for a first course in linear algebra for undergraduate students in all disciplines. It can be also used as a booklet for graduate students, allowing to acquire some concepts, examples, and basic results. It is also suitable for those students who are looking for a simple, easy, and clear textbook that summarizes the main ideas of linear algebra.