Understanding Linear Algebra by David Austin
Understanding Linear Algebra - Table of Contents
- 1. Systems of Equations
- 2. Vectors, Matrices, and Linear Combinations
- 3. Invertibility, Bases, and Coordinate Systems
- 4. Eigenvalues and Eigenvectors
- 5. Linear Algebra and Computing
- 6. Orthogonality and Least Squares
- 7. Singular Value Decompositions
What You Will Learn in Understanding Linear Algebra
This book focuses on helping learners grasp the core concepts of linear algebra without requiring prior knowledge of calculus. The text emphasizes active learning through interactive activities and exercises, encouraging students to develop their mathematical reasoning skills. It also integrates computational tools like SageMath, making it an excellent open-source linear algebra textbook with computational tools that allows students to perform calculations directly within the text. Real-world applications, such as image compression and Google's PageRank algorithm, are included to demonstrate the practical relevance of linear algebra.
As a comprehensive resource, Understanding Linear Algebra David Austin edition is an open textbook designed to support a two-course undergraduate linear algebra sequence. If you want to learn linear algebra concepts step-by-step, this text covers essential topics including systems of equations, vector and matrix algebra, span, linear independence, bases, eigenvectors and eigenvalues, orthogonality, least squares, and singular value decompositions. It serves as a complete introduction to university-level mathematics for modern students.
Until recently, linear algebra has mainly lived in the long shadow of calculus, with many university courses requiring several semesters of calculus as a prerequisite. Given the increasing prominence of this subject, this text assumes no familiarity with calculus, providing a highly recommended free linear algebra textbook for beginners. This book arises from the belief that linear algebra, as presented in a traditional undergraduate curriculum, has for too long lived in the shadow of calculus, making it a perfect linear algebra study guide for self-learners worldwide.
Book Details & Specifications
Title:
Understanding Linear Algebra by David Austin
Publisher:
Wreath
Year:
2023
Pages:
517
Type:
PDF
Language:
English
ISBN-10 #:
1958469165
ISBN-13 #:
978-1958469163
License:
CC BY 4.0
Amazon:
Amazon
About the Author: David Austin
The author David Austin
is a Professor of Mathematics at Grand Valley State University, well known for his work on linear algebra textbooks for mathematics students. In his work, he explains difficult ideas step by step, creating a beginner-friendly guide to linear algebra that makes it easier for self-learners to master complex concepts.
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