Lectures on Clifford (Geometric) Algebras and Applications
Contributors: Rafal Ablamowicz (Editor); Garret Sobczyk (Editor)
Edition: 1 edition
Publisher: Birkhäuser Boston
Published: November 6, 2003
Language: eng
Format: Paperback
Number of pages: 221
ISBN-13: 9780817632571
Subjects: Algebra; Geometry; Science/Mathematics; Geometry - Algebraic; Mathematics; Mathematics / Geometry / Differential; Clifford algebras; Algebra - General; Mathematical Physics
First sentence: ABSTRACT Clifford algebras of lower-dimensional Euclidean spaces and Min-kowski spacetime are discussed and identified with their matrix images.
Description: The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts underlying the mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. This bird's-eye view of Clifford (geometric) algebras and their applications is presented by six of the world's leading experts in the field. Key topics and features of this systematic exposition: * An Introductory chapter on Clifford Algebras by Pertti Lounesto * Ian Porteous (Chapter 2) reveals the mathematical structure of Clifford algebras in terms of the classical groups * John Ryan (Chapter 3) introduces the basic concepts of Clifford analysis, which extends the well-known complex analysis of the plane to three and higher dimensions * William Baylis (Chapter 4) investigates some of the extensive applications that have been made in mathematical physics, including the basic ideas of electromagnetism and special relativity * John Selig (Chapter 5) explores the successes that Clifford algebras, especially quaternions and bi-quaternions, have found in computer vision and robotics * Tom Branson (Chapter 6) discusses some of the deepest results that Clifford algebras have made possible in our understanding of differential geometry * Editors (Appendix) give an extensive review of various software packages for computations with Clifford algebras including standalone programs, on-line calculators, special purpose numeric software, and symbolic add-ons to computer algebra systems This text will serve beginning graduate students and researchers in diverse areas---mathematics, physics, computer science and engineering; it will be useful both for newcomers who have little prior knowledge of the subject and established professionals who wish to keep abreast of the latest applications.