Matrix Algebra: Theory, Computations, and Applications in Statistics Third Edition

by James E. Gentle

Springer, 2024

This book covers the theory of matrices and linear algebra for applications in statistics. It also covers the basics of numerical analysis for computations involving vectors and matrices.

The outline is

• Preface
• Table of Contents
  • 1. Introduction
• I. Linear Algebra
  • 2. Vectors and Vector Spaces
  • 3. Basic Properties of Matrices
  • 4. Matrix Transformations and Factorizations
  • 5. Solution of Linear Systems
  • 6. Evaluation of Eigenvalues and Eigenvectors
  • 7. Real Analysis and Probability Distributions of Vectors and Matrices
• II. Applications in Statistics and Data Science
  • 8. Special Matrices and Operations Useful in Modeling and Data Science
  • 9. Selected Applications in Statistics
• III. Numerical Methods and Software
  • 10. Numerical Methods
  • 11. Numerical Linear Algebra
  • 12. Software for Numerical Linear Algebra
• Bibliography
• Subject Index

Errata.

Hints and solutions to selected exercises.

I would appreciate any feedback from readers -- corrections, suggestions, or general comments.

James Gentle, jgentle@gmu.edu