Interactive Linear Algebra - Overview Notes

Authors and Affiliation

• Authors: Dan Margalit and Joseph Rabinoff
• Affiliation: School of Mathematics, Georgia Institute of Technology
• Publication Date: June 3, 2019

Main Content Overview

The textbook is structured into several key parts, each focusing on different aspects of linear algebra:

1. Systems of Linear Equations: Algebra

• Understanding systems of linear equations
• Techniques in row reduction
• Parametric form of solutions

2. Systems of Linear Equations: Geometry

• Concepts of vectors and vector equations
• Understanding matrix equations and solution sets
• Concepts of linear independence and subspaces
• Exploring basis and dimension
• Usage of bases as coordinate systems
• The Rank Theorem

3. Linear Transformations and Matrix Algebra

• Exploring matrix transformations
• Concepts of one-to-one and onto transformations
• Detailed study on linear transformations
• Matrix operations including multiplication
• Understanding matrix inverses and the Invertible Matrix Theorem

4. Determinants

• Definition and properties of determinants
• Techniques of cofactor expansions
• Relationship between determinants and volumes

5. Eigenvalues and Eigenvectors

• Introduction to eigenvalues and eigenvectors
• Understanding the characteristic polynomial
• Concepts of similarity and diagonalization
• Study of complex eigenvalues and stochastic matrices

6. Orthogonality

• Understanding dot products and orthogonality
• Exploring orthogonal complements and projections
• Learning about orthogonal sets and the method of least squares

Additional Resources

• Colophon, contributors, and variants sections provide further context and background.
• Interactive feedback and suggestions can be submitted via GitHub.
• The back matter includes complex numbers, notations, hints, and solutions to exercises, and licensing information.

Navigation and Licensing

• The textbook offers a comprehensive index for easy navigation.
• Licensed under the GNU Free Documentation License, promoting free access and sharing.