Basic Matrix Algebra With Algorithms and Applications: A Foundational Linear Algebra Textbook by Robert A. Liebler

Introduction

Linear algebra is the language of modern mathematics and data science, yet many students find it intimidating. Basic Matrix Algebra With Algorithms and Applications by Robert A. Liebler is a refreshingly approachable guide that builds a solid foundation in matrix algebra without overwhelming abstraction. Published by Chapman and Hall/CRC, this hardcover edition is designed for Indian undergraduate students and professionals who need to understand linear models for their coursework or research. With clear explanations, visual learning aids, and a focus on computational techniques, this book bridges the gap between theory and real-world application.

Book Overview

This book presents linear algebra through the lens of matrix computations, algorithms, and practical examples. Liebler avoids unnecessary formalism and instead emphasises minimal polynomials and their computation using the Krylov algorithm—a powerful yet often overlooked tool. The text is organised into short, digestible sections that allow readers to progress at their own pace. A graphing calculator is used throughout to shift focus from tedious arithmetic to conceptual understanding, making it ideal for self-study or classroom use. The book also provides downloadable Maple worksheets for further practice and exploration.

Key Highlights

• Algorithmic approach: Learn matrix algebra through step-by-step algorithms that are easy to follow and implement.
• Krylov method focus: Unique emphasis on minimal polynomials and Krylov subspace techniques for computing eigenvalues and eigenvectors.
• Visual and practical: Heavy reliance on graphing calculators and visualisation to demystify abstract concepts.
• Bite-sized chapters: Short, focused sections that make learning manageable and retention easier.
• Real-world relevance: Applications drawn from natural resources, social sciences, business, and other disciplines that use linear models.

Inside the Book

The book begins with the basics of matrices and vectors, then moves through systems of linear equations, determinants, eigenvalues, and eigenvectors. Each concept is introduced with concrete examples and computational exercises. Special attention is given to the Krylov algorithm for computing minimal polynomials, a topic rarely covered in introductory texts. Later chapters explore applications such as Markov chains, linear regression, and population dynamics. The writing is conversational and free of unnecessary jargon, making complex ideas accessible to students from diverse backgrounds.

Key Topics

• Matrix operations and properties
• Solving linear systems using Gaussian elimination and LU decomposition
• Determinants and their geometric interpretation
• Vector spaces, subspaces, and linear independence
• Eigenvalues, eigenvectors, and diagonalisation
• Minimal polynomials and the Krylov algorithm
• Inner products, orthogonality, and least squares
• Applications to Markov chains, linear regression, and dynamical systems

Reader Benefits

• Gain a solid grasp of matrix algebra without getting lost in abstract theory.
• Develop practical computational skills using algorithms and calculators.
• Understand how linear algebra applies to real-world problems in science, business, and engineering.
• Build confidence for advanced courses in data science, machine learning, operations research, and more.
• Access supplementary materials (Maple worksheets) to reinforce learning through hands-on practice.

Learning Outcomes

By the end of this book, readers will be able to: perform matrix operations with confidence; solve systems of linear equations using multiple methods; compute determinants and interpret their meaning; find eigenvalues and eigenvectors using both standard and Krylov-based techniques; understand the concept of minimal polynomials; apply linear algebra to model and solve problems in various fields; and use computational tools to verify results and explore deeper concepts.

Who Should Read

This book is ideal for first-year undergraduate students in mathematics, statistics, physics, and engineering. It is also highly suitable for upper-level students in natural resources, social sciences, business, economics, and any discipline that eventually requires working with linear models. Instructors looking for a student-friendly textbook that emphasises algorithms and applications will find this a valuable resource. Self-learners and professionals returning to mathematics will appreciate the clear, step-by-step presentation.

About the Author

Robert A. Liebler is a mathematician and educator with decades of experience teaching linear algebra and related subjects. His writing reflects a deep understanding of student challenges and a commitment to making mathematics accessible. Liebler’s approach combines rigorous content with pedagogical clarity, ensuring that readers not only learn the material but also enjoy the journey.

About the Publisher

Chapman and Hall/CRC is a premier academic publisher known for high-quality textbooks and reference works in mathematics, statistics, and applied sciences. With a legacy of excellence spanning decades, CRC Press—now part of the Taylor & Francis Group—continues to support learners and researchers worldwide with authoritative, well-crafted books that stand the test of time.

Conclusion

Basic Matrix Algebra With Algorithms and Applications is more than just a textbook—it is a companion for anyone who wants to truly understand linear algebra. With its unique algorithmic focus, visual teaching style, and real-world examples, this book empowers readers to master matrix algebra and apply it with confidence. Whether you are a student in India preparing for competitive exams or a professional seeking to strengthen your quantitative skills, this hardcover edition is a worthy addition to your library. Order your copy from Bookshops.in today and start your journey into the elegant world of matrices.