Advanced Linear Algebra

Advanced Linear Algebra is a textbook designed for advanced undergraduate and beginning graduate students in linear or abstract algebra. It covers theoretical aspects of the subject, examples, computations, and proofs, and explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. Each chapter consists of a mathematical vignette devoted to the development of one specific topic, and the book provides a bridge from elementary computational linear algebra to more advanced, abstract aspects of linear algebra needed in many areas of pure and applied mathematics.

Format: Hardback
Length: 634 pages
Publication date: 21 June 2024
Publisher: Taylor & Francis Ltd

Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra delves into the theoretical aspects of the subject, accompanied by examples, computations, and proofs. It explores a diverse range of advanced topics in linear algebra, highlighting the profound interconnections of the field with geometry, algebra, analysis, combinatorics, numerical computation, and numerous other branches of mathematics.

The author begins by introducing fundamental notation for vector spaces, permutations, polynomials, and other algebraic structures. The subsequent chapters are designed to be largely independent of each other, allowing readers with varying interests to jump directly to the topic of their choice. This unconventional organization sets Advanced Linear Algebra apart from many abstract algebra textbooks, which mandate a sequential chapter order.

Each chapter comprises a mathematical vignette dedicated to the development of a specific topic. Some chapters present introductory material from a sophisticated or abstract perspective, while others offer elementary expositions of more theoretical concepts. Several chapters offer unique perspectives or novel treatments of established results.

A wide array of topics is covered, spanning from concrete matrix theory (basic matrix computations, determinants, normal matrices, canonical forms, matrix factorizations, and numerical algorithms) to more abstract linear algebra (modules, Hilbert spaces, dual vector spaces, bilinear forms, principal ideal domains, universal mapping properties, and multilinear algebra).

The book serves as a bridge from elementary computational linear algebra to more advanced, abstract aspects of linear algebra required in many areas of pure and applied mathematics.

Weight: 1370g
Dimension: 254 x 178 (mm)
ISBN-13: 9781032765723
Edition number: 2 ed