A First Course in Linear Algebra

A First Course in Linear Algebra is written by two experts from algebra who have more than 20 years of experience in algebra, linear algebra and number theory. It prepares students with no background in Linear Algebra. Students, after mastering the materials in this textbook, can already understand any Linear Algebra used in more advanced books and research papers in Mathematics or in other scientific disciplines.

This book provides a solid foundation for the theory dealing with finite dimensional vector spaces. It explains in details the relation between linear transformations and matrices. One may thus use different viewpoints to manipulate a matrix instead of a one-sided approach. Although most of the examples are for real and complex matrices, a vector space over a general field is briefly discussed. Several optional sections are devoted to applications to demonstrate the power of Linear Algebra.

Contents:

• Preface
• Vector Spaces
• Bases and Dimension
• Linear Transformations and Matrices
• Elementary Matrix Operations
• Diagonalization
• Canonical Forms
• Inner Product Spaces

Readership: Undergraduates who are interested in learning linear algebra and its applications.
Key Features:

• This book uses straightforward and simple English and is especially useful for students who are not native speakers of English
• The amount of exercises in this book provide a rigorous coverage of the subject compared to most of the textbooks in the market
• This textbook is theoretically oriented while it also includes applications to show the power of Linear Algebra