Quaternions And Cayley Numbers
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Quaternions And Cayley Numbers
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Author : J.P. Ward
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quaternions And Cayley Numbers written by J.P. Ward 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 2012-12-06 with Mathematics categories.
In essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics - particularly relativity and electromagnetism - generally the mathematics is not sophisticated. In fact, the mathematically sophisticated reader, may well find that in many places, the rather deliberate progress too slow for their liking. This text had its origin in a 90-minute lecture on complex numbers given by the author to prospective university students in 1994. In my attempt to develop a novel approach to the subject matter I looked at complex numbers from an entirely geometric perspective and, no doubt in line with innumerable other mathematicians, re-traced steps first taken by Hamilton and others in the early years of the nineteenth century. I even enquired into the possibility of using an alternative multiplication rule for complex numbers (in which argzlz2 = argzl- argz2) other than the one which is normally accepted (argzlz2 = argzl + argz2). Of course, my alternative was rejected because it didn't lead to a 'product' which had properties that we now accept as fundamental (i. e.
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
Historical Aspects Of Complex Quaternions And Cayley Numbers
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Author : Marilyn M. Simmons
language : en
Publisher:
Release Date : 1992
Historical Aspects Of Complex Quaternions And Cayley Numbers written by Marilyn M. Simmons and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Numbers, Complex categories.
Construction Of Quaternions And Cayley Numbers As Examples Of Linear Algebras
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Author : Marlene Tellinghuisen Tate
language : en
Publisher:
Release Date : 1964
Construction Of Quaternions And Cayley Numbers As Examples Of Linear Algebras written by Marlene Tellinghuisen Tate and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Algebras, Linear categories.
The Geometry Of The Octonions
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Author : Tevian Dray
language : en
Publisher: World Scientific
Release Date : 2015
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 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.Contents: Introduction"Number Systems: "The Geometry of the Complex NumbersThe Geometry of the QuaternionsThe Geometry of the OctonionsOther Number Systems"Symmetry Groups: "Some Orthogonal GroupsSome Unitary GroupsSome Symplectic GroupsSymmetry Groups over Other Division AlgebrasLie Groups and Lie AlgebrasThe Exceptional Groups"Applications: "Division Algebras in MathematicsOctonionic Eigenvalue ProblemsThe Physics of the OctonionsMagic Squares Readership: Advanced ubdergraduate and graduate students and faculty in mathematics and physics; non-experts with moderately sophisticated mathematics background. Key Features: This book is easily digestible by a large audience wanting to know the elementary introduction to octanionsSuitable for any reader with a grasp of the complex numbers, although familiarity with non-octonionic versions of some of the other topics would be helpfulMany open problems are very accessibleAdvanced topics covered are quite sophisticated, leading up to a clear discussion of (one representation of) the exceptional Lie algebras and their associated root diagrams, and of the octonionic projective spaces on which they act
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.
Spinors Clifford And Cayley Algebras
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Author : Robert Hermann
language : en
Publisher: Math-Sci Press
Release Date : 1974
Spinors Clifford And Cayley Algebras written by Robert Hermann and has been published by Math-Sci Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Extension Of Some Theorems Of Complex Functional Analysis To Linear Spaces Over The Quaternions And Cayley Numbers
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Author : James E. Jamison
language : en
Publisher:
Release Date : 1970
Extension Of Some Theorems Of Complex Functional Analysis To Linear Spaces Over The Quaternions And Cayley Numbers written by James E. Jamison and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Banach spaces categories.
"In this work certain aspects of Functional Analysis are considered in the setting of linear spaces over the division rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are given. Questions concerning linear functionals, the Hahn-Banach Theorem and Reflexivity are considered. The Stone-Weierstrass Theorem is proven for functions with values in a real Cayley Dickson algebra of dimension n. The concepts of inner product spaces and Hilbert spaces over the Quaternions and the Cayley algebra are developed. An extensive study of Hilbert spaces over the Quaternions is carried out. In the case of Hilbert spaces over the Quaternions, the Riesz-Representation Theorem and the Jordan-von Neumann Theorem are proven. In addition, spectral theorems for both self-adjoint and normal operators are proven for finite dimensional Hilbert spaces. These results are extended to infinite dimensional spaces for the cases of compact self-adjoint operators and compact normal operators. The spectrum of an arbitrary bounded Hermitian operator on a Hilbert space over the Quaternions is shown to be non-void. A generalization of the Fourier Transform for functions in L[1 over Q](-infinity, infinity) and L[2 over Q]( ](-infinity, infinity) is given. The Plancherel Theorem is proven for functions in L[2 over Q](-infinity, infinity). Finally, the Jordan-von Neumann theorem is proven for a Hilbert space over the Cayley algebra"--Abstract, pages ii-iii.
Introduction To Quaternions With Numerous Examples
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Author : Philip Kelland
language : en
Publisher:
Release Date : 1873
Introduction To Quaternions With Numerous Examples written by Philip Kelland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1873 with Quaternions categories.
Hypercomplex Numbers
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Author : Isaĭ Lʹvovich Kantor
language : en
Publisher:
Release Date : 1989
Hypercomplex Numbers written by Isaĭ Lʹvovich Kantor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Numbers, Complex categories.