Welcome to Jeff Anderson’s Applied Linear Algebra Fundamentals (ALAF) textbook project homepage.
Here you will find my larger vision for this work, links to my most recent content, and other resources to support excellent applied linear algebra curriculum that I make available to the world for no required paywall.
If you enjoy this work, please check out my support page to learn more about how you can become part a larger community of people who help to transform this dream into a reality.
Front Matter
Warm Up
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Table of Contents (.pdf) | Version 000.1 - 10/20/2025 |
Notation Guide | None |
How to Report Errors and Edits? | None |
Welcome to the Party
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Preface | None |
Forward | None |
Introduction (.pdf) | Version 000.1 - 10/20/2025 |
To the Students | None |
To Research Educators | None |
Join the Community
Lesson Title and Resources |
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How Can You Support This Project? | None |
How Can You Join the ALAF Creative Team? | None |
Acknowledgements | None |
Part 0: Background Theory
Fundamentals of Mathematical Modeling
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Introduction to Applied Modeling
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Version 000.1 - 10/20/2025 |
Different Types of Mathematical Models | None |
The Major Problems of Linear Algebra | None |
The Three Pillars of Applied Mathematics | None |
Applied Linear Algebra Models
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Applied Linear Algebraic Models of Real Mass-Spring Systems | None |
Applied Linear Algebraic Models of Real Electric Circuits | None |
Applied Linear Algebraic Models in Image Processing | None |
Part 1: The Matrix-Vector Multiplication Problem
Vectors and Vector Operations
Hello, World!
Matrices and Matrix Operations
Hello, World!
The Matrix-Vector Multiplication Problem
Hello, World!
Part 2: The Linear-Systems Problem
The Nonsingular Linear-Systems Problem
Hello, World!
Matrix Factorizations for Nonsingular Linear Systems
Hello, World!
The Best Introduction to Determinants on All of YouTube
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Discover the Determinant Function | None |
Three Mysteries in Permutations
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Version 000.1 - 10/07/2025 |
The General Determinant Function and Its Children | None |
Properties of Determinants | None |
Practical Considerations - Introduction to Calculating Determinants | None |
The General Linear Systems Problem
Hello, World!
Specialized Approaches to Solving Linear Systems
Hello, World!
Error Analysis for Linear Systems
Hello, World!