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
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How to Report Errors and Edits?
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Welcome to the Party


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Preface
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Forward
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Introduction (.pdf)
Version 000.1 - 10/20/2025
To the Students
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To Research Educators
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Join the Community


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How Can You Support This Project?
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How Can You Join the ALAF Creative Team?
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Acknowledgements
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Part 0: Background Theory

Fundamentals of Mathematical Modeling


Lesson Title and Resources
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Introduction to Applied Modeling

  1. Intro to Applied Modeling YouTube Playlist link
  2. Intro to Math Modeling: Lesson Notes (.pdf)
  3. Intro to Applied Modeling Student Solution Sets (.pdf)

Version 000.1 - 10/20/2025
Different Types of Mathematical Models
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The Major Problems of Linear Algebra
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The Three Pillars of Applied Mathematics
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Applied Linear Algebra Models


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Applied Linear Algebraic Models of Real Mass-Spring Systems
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Applied Linear Algebraic Models of Real Electric Circuits
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Applied Linear Algebraic Models in Image Processing
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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
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Three Mysteries in Permutations

  1. Three Mysteries in Permutations YouTube Playlist link
  2. Three Mysteries in Permutations : Lesson Notes (.pdf)
  3. Three Mysteries in Permutations: Student Solution Sets (.pdf)
  4. Three Mysteries in Permutations: GitHub Repository

Version 000.1 - 10/07/2025
The General Determinant Function and Its Children
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Properties of Determinants
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Practical Considerations - Introduction to Calculating Determinants
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The General Linear Systems Problem

Hello, World!

Specialized Approaches to Solving Linear Systems

Hello, World!

Error Analysis for Linear Systems

Hello, World!

Part 3: The Full-Rank Least Squares Problem

Part 4: The Standard Eigenvalue Problem and Beyond