A Concise Introduction to Linear Algebra

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Springer Science & Business Media, Mar 30, 2012 - Mathematics - 330 pages
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Building on the author's previous edition on the subject (Introduction to Linear Algebra, Jones & Bartlett, 1996), this book offers a refreshingly concise text suitable for a standard course in linear algebra, presenting a carefully selected array of essential topics that can be thoroughly covered in a single semester. Although the exposition generally falls in line with the material recommended by the Linear Algebra Curriculum Study Group, it notably deviates in providing an early emphasis on the geometric foundations of linear algebra. This gives students a more intuitive understanding of the subject and enables an easier grasp of more abstract concepts covered later in the course.

The focus throughout is rooted in the mathematical fundamentals, but the text also investigates a number of interesting applications, including a section on computer graphics, a chapter on numerical methods, and many exercises and examples using MATLAB. Meanwhile, many visuals and problems (a complete solutions manual is available to instructors) are included to enhance and reinforce understanding throughout the book.

Brief yet precise and rigorous, this work is an ideal choice for a one-semester course in linear algebra targeted primarily at math or physics majors. It is a valuable tool for any professor who teaches the subject.

 

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Decent book to use for a beginner linear algebra course, but better options are available (Axler's Linear Algebra Done Right and Strang's Linear Algebra and its Applications).
While the material
presented within this textbook is accurate and informative, the book is too dense for many non-mathematics students to derive much value from. Theorems are presented in rapid succession throughout, with too little descriptive text tying them together. In a course required for so many other majors, this book falls short and leaves many students turning to more accessible information on Youtube and other texts that are outwardly more conversational in tone.
Schay's Concise Introduction to Linear Algebra will however make a fine addition to and can be used in conjunction with most other linear algebra texts, and will retain value beyond the duration of the course as a desk reference for undergraduate mathematics students.
 

Contents

1 Analytic Geometry of Euclidean Spaces
1
2 Systems of Linear Equations Matrices
41
3 Vector Spaces and Subspaces
99
4 Linear Transformations
163
5 Orthogonal Projections and Bases
199
6 Determinants
221
7 Eigenvalues and Eigenvectors
253
8 Numerical Methods
291
A Appendices
315
Further Reading
325
Index
327
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