On Quaternions And Octonions
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On Quaternions And Octonions
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Author : John H. Conway
language : en
Publisher: CRC Press
Release Date : 2003-01-23
On Quaternions And Octonions written by John H. Conway and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-23 with Mathematics categories.
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less f
On Quaternions And Octonions
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Author : John Horton Conway
language : en
Publisher:
Release Date : 2005
On Quaternions And Octonions written by John Horton Conway and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
On Quaternions And Octonions
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Author : John H. Conway
language : en
Publisher: A K Peters/CRC Press
Release Date : 2003-01-23
On Quaternions And Octonions written by John H. Conway and has been published by A K Peters/CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-23 with Mathematics categories.
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane.
Division Algebras
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Author : G.M. Dixon
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Division Algebras written by G.M. Dixon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
I don't know who Gigerenzer is, but he wrote something very clever that I saw quoted in a popular glossy magazine: "Evolution has tuned the way we think to frequencies of co-occurances, as with the hunter who remembers the area where he has had the most success killing game." This sanguine thought explains my obsession with the division algebras. Every effort I have ever made to connect them to physics - to the design of reality - has succeeded, with my expectations often surpassed. Doubtless this strong statement is colored by a selective memory, but the kind of game I sought, and still seek, seems to frowst about this particular watering hole in droves. I settled down there some years ago and have never feIt like Ieaving. This book is about the beasts I selected for attention (if you will, to ren der this metaphor politically correct, let's say I was a nature photographer), and the kind of tools I had to develop to get the kind of shots Iwanted (the tools that I found there were for my taste overly abstract and theoretical). Half of thisbook is about these tools, and some applications thereof that should demonstrate their power. The rest is devoted to a demonstration of the intimate connection between the mathematics of the division algebras and the Standard Model of quarks and leptons with U(l) x SU(2) x SU(3) gauge fields, and the connection of this model to lO-dimensional spacetime implied by the mathematics.
The Geometry Of The Octonions
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Author : Tevian Dray
language : en
Publisher: World Scientific
Release Date : 2015-04-08
The Geometry Of The Octonions written by Tevian Dray and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-08 with Mathematics categories.
There are precisely two further generalizations of the real and complex numbers, namely, the quaternions and the octonions. The quaternions naturally describe rotations in three dimensions. In fact, all (continuous) symmetry groups are based on one of these four number systems. This book provides an elementary introduction to the properties of the octonions, with emphasis on their geometric structure. Elementary applications covered include the rotation groups and their spacetime generalization, the Lorentz group, as well as the eigenvalue problem for Hermitian matrices. In addition, more sophisticated applications include the exceptional Lie groups, octonionic projective spaces, and applications to particle physics including the remarkable fact that classical supersymmetry only exists in particular spacetime dimensions.
Octonions
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Author : Alexander McAulay
language : en
Publisher:
Release Date : 1898
Octonions written by Alexander McAulay and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1898 with Clifford algebras categories.
Quaternion And Octonion Color Image Processing With Matlab
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Author : Artyom M. Grigoryan
language : en
Publisher:
Release Date : 2018
Quaternion And Octonion Color Image Processing With Matlab written by Artyom M. Grigoryan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with TECHNOLOGY & ENGINEERING categories.
"Color image processing has involved much interest in the recent years. The use of color in image processing is motivated by the facts that 1) the human eyes can discern thousands of colors, and image processing is used both for human interaction and computer interpretation; 2) the color image comprises more information than the gray-level image; 3) the color features are robust to several image processing procedures (for example, to the translation and rotation of the regions of interest); 4) the color features are efficiently used in many vision tasks, including object recognition and tracking, image segmentation and retrieval, image registration etc.; 5) the color is necessary in many real life applications such as visual communications, multimedia systems, fashion and food industries, computer vision, entertainment, consumer electronics, production printing and proofing, digital photography, biometrics, digital artwork reproduction, industrial inspection, and biomedical applications. Finally, the enormous number of color images that constantly are uploaded into Internet require new approaches and challenges of big visual media creation, retrieval, processing, and applications. It also gives us new opportunities to create a number of big visual data-driven applications. Three independent quantities are used to describe any particular color; the human eyes are seen all colors as variable combinations of primary colors of red, green, and blue. Many methods of the modern color image processing are based on dealing out each primary color"--
Visualizing Quaternions
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Author : Andrew J. Hanson
language : en
Publisher: Elsevier
Release Date : 2006-02-06
Visualizing Quaternions written by Andrew J. Hanson and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-06 with Mathematics categories.
Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available. The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. Covers both non-mathematical and mathematical approaches to quaternions.
On Quaternions And Octonions
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Author : John H. Conway
language : en
Publisher: CRC Press
Release Date : 2003-01-23
On Quaternions And Octonions written by John H. Conway and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-23 with Mathematics categories.
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less f
Rotations Quaternions And Double Groups
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Author : Simon L. Altmann
language : en
Publisher: Courier Corporation
Release Date : 2013-04-09
Rotations Quaternions And Double Groups written by Simon L. Altmann and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems. Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. Some familiarity with the basics of group theory is assumed, but the text assists students in developing the requisite mathematical tools as necessary.