Introduction to Linear Algebra International 4th Edition
Table of Contents
- Chapter 1. Introduction to Vectors
- Chapter 2. Solving Linear Equations
- Chapter 3. Vector Spaces and Subspaces
- Chapter 4. Orthogonality
- Chapter 5. Determinants
- Chapter 6. Eigenvalues and Eigenvectors
- Chapter 7. Linear Transformations
- Chapter 8. Applications
- Chapter 9. Numerical Linear Algebra
- Chapter 10. Complex Vectors and Matrices
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This textbook is an introduction to the ideals and techniques of linear algebra for first- or second-year students with a working knowledge of high school algebra. The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1-4 contain a one-semester course for beginners whereas Chapter 5-9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (review in Appendix A). Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. Calculus is not a prerequisite; places where it is mentioned may by omitted.
As a rule, students of linear algebra learn by studying examples and solving problems. Accordingly, the book contains a variety of exercises (over 1200, many with multiple parts), ordered as to their difficulty. In addition, more than 375 solved examples are included in the text, many of which are computational in nature.
For courses in Advanced Linear Algebra. This top-selling, theorem-proof text presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate.
For courses in linear algebra. With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students’ understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rn setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand. MyMathLab not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information. MyMathLab is an online homework, tutorial, and assessment product designed to personalize learning and improve results. With a wide range of interactive, engaging, and assignable activities, students are encouraged to actively learn and retain tough course concepts.
About the Author
David I. Spivak is a Research Scientist in the Department of Mathematics at MIT.