Fundamentals of Linear Algebra

Fundamentals of Linear Algebra is a unique book on the subject, covering more material in less pages than other books. It defines the dimension of a vector space as its Krull dimension, which simplifies the understanding of bases and their number of vectors. The book includes theories and applications across arbitrary fields and offers non-trivial examples to address real-world problems.

Format: Paperback / softback
Length: 240 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

The Fundamentals of Linear Algebra stands out as a remarkable resource on the subject, offering a unique and comprehensive approach. In just under 250 pages, it has managed to cover the topic more thoroughly than books with twice as many pages. For instance, the textbooks commonly used in the United States provide evidence of a basis for finite-dimensional vector spaces. This book goes beyond that, demonstrating the existence of a basis for any given vector space.

The author, with their expertise in algebraic geometry and commutative algebra, introduces a novel definition of the dimension of a vector space: the Krull dimension. By adopting this definition, numerous facts about bases in finite-dimensional spaces become straightforward consequences. For instance, the replacement theorem becomes unnecessary, as it becomes evident that any two bases of a finite-dimensional vector space contain the same number of vectors. Furthermore, this definition of dimension holds true even when dealing with nonlinear geometric objects.

This book offers a wealth of features designed to enhance the learning experience and improve outcomes. It presents theories and applications, aiming to raise expectations and foster a deeper understanding of the subject. The coverage spans arbitrary fields, making it applicable to a wide range of mathematical disciplines. Additionally, numerous non-trivial examples are included, addressing real-world problems and demonstrating the practical applications of linear algebra.

In summary, The Fundamentals of Linear Algebra is a exceptional book that provides a comprehensive and unified approach to the subject. Its concise yet thorough coverage, coupled with innovative definitions and practical examples, makes it an invaluable resource for students and professionals alike. Whether you are a beginner or an advanced mathematician, this book will help you deepen your understanding of linear algebra and its applications in various fields.

Weight: 440g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032475813