Lectures on Clifford Geometric Algebras and Applications （2003. 250 S.）

Ed. by Rafa Abamowicz and Garret Sobczyk

BIRKHÄUSER（2003発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 250 p.
• 商品コード 9780817632571

Full 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 systemsThis 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.