About the Book
- Page ID
- 181861
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This Mathematics textbook is part of the De Anza College Zero Textbook Cost (ZTC) Pathways initiative, supporting both students and instructors with free, adaptable Open Educational Resources (OER).
This book offers a comprehensive and accessible introduction to linear algebra. It begins with methods for solving linear systems, followed by an exploration of matrices and their properties, including a dedicated chapter on determinants. The text then introduces vectors in Rn\mathbb{R}^nRn, covering essential concepts such as span, linear independence, subspaces, and linear transformations. From there, it develops spectral theory, including diagonalization and orthogonal diagonalization, along with their applications. The final chapter explores general vector spaces and revisits core linear algebra concepts in that broader context. With numerous examples and practical applications, the material is designed to engage students and support their development in applying abstract mathematical ideas to problem solving—making it a valuable resource for both individual study and classroom use.
This book builds upon the foundation established in A Course in Linear Algebra by Ken Kuttler, one of the most widely used open educational resources in the subject. Additional material was drawn from three other sources: the Gauss-Seidel method from Autar Kaw’s Introduction to Matrix Algebra, determinant geometry from Dan Margalit and Joseph Rabinoff’s Interactive Linear Algebra, and inner product spaces from W. Keith Nicholson’s Linear Algebra with Applications. We also acknowledge Lake Tahoe Community College’s derivative of Kuttler’s textbook, which incorporates video resources and served as an important starting point for our own work. In creating this resource, we have aimed to uphold the principles of open education while enhancing accessibility for a diverse range of learners.
In addition to the core text, we provide ancillary materials to enhance teaching and learning.
Included Ancillary Materials
- Instructor Notes: Guidance for educators with teaching tips, common misconceptions, and activity ideas.
This ancillary can be found under “assets” on the De Anza Commons page for Linear Algebra: A First Course
Online Homework
Aligned online homework is available on MyOpenMath. After logging into an instructor account, select Add New Course → Copy a template or promoted course → choose Calculus I: Differential Calculus (De Anza ZTC).