Linear Algebra

Nonfiction, Science & Nature, Mathematics, Algebra
Cover of the book Linear Algebra by Belkacem Said-Houari, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Belkacem Said-Houari ISBN: 9783319637938
Publisher: Springer International Publishing Publication: October 4, 2017
Imprint: Birkhäuser Language: English
Author: Belkacem Said-Houari
ISBN: 9783319637938
Publisher: Springer International Publishing
Publication: October 4, 2017
Imprint: Birkhäuser
Language: English

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.  

The book includes a set of exercises at the end of each chapter, which have been carefully chosen to illustrate the main ideas. Some of them were taken (with some modifications) from recently published papers, and appear in a textbook for the first time. Detailed solutions are provided for every exercise, and these refer to the main theorems in the text when necessary, so students can see the tools used in the solution.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.  

The book includes a set of exercises at the end of each chapter, which have been carefully chosen to illustrate the main ideas. Some of them were taken (with some modifications) from recently published papers, and appear in a textbook for the first time. Detailed solutions are provided for every exercise, and these refer to the main theorems in the text when necessary, so students can see the tools used in the solution.

More books from Springer International Publishing

Cover of the book Essays on the Frontiers of Modern Astrophysics and Cosmology by Belkacem Said-Houari
Cover of the book Recent Advancements in Materials and Systems for Thermal Energy Storage by Belkacem Said-Houari
Cover of the book Performing Character in Modern Irish Drama by Belkacem Said-Houari
Cover of the book Charge Multiplicity Asymmetry Correlation Study Searching for Local Parity Violation at RHIC for STAR Collaboration by Belkacem Said-Houari
Cover of the book SmartParticipation by Belkacem Said-Houari
Cover of the book Accurate and Robust Spectral Testing with Relaxed Instrumentation Requirements by Belkacem Said-Houari
Cover of the book Leading Successfully in Asia by Belkacem Said-Houari
Cover of the book Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications by Belkacem Said-Houari
Cover of the book Is ‘Fuzzy Theory’ an Appropriate Tool for Large Size Problems? by Belkacem Said-Houari
Cover of the book Numeric Computation and Statistical Data Analysis on the Java Platform by Belkacem Said-Houari
Cover of the book Recent Developments and New Direction in Soft-Computing Foundations and Applications by Belkacem Said-Houari
Cover of the book Complements of Higher Mathematics by Belkacem Said-Houari
Cover of the book Handbook of Ripple Effects in the Supply Chain by Belkacem Said-Houari
Cover of the book Interdisciplinary Applications of Kinematics by Belkacem Said-Houari
Cover of the book Termites and Sustainable Management by Belkacem Said-Houari
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy