Quaternions And Cayley Numbers PDF Download
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Author | : J.P. Ward |
Publisher | : Springer Science & Business Media |
Total Pages | : 252 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401157685 |
Download Quaternions and Cayley Numbers Book in PDF, ePub and Kindle
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.
Author | : John H. Conway |
Publisher | : CRC Press |
Total Pages | : 110 |
Release | : 2003-01-23 |
Genre | : Mathematics |
ISBN | : 1000687775 |
Download On Quaternions and Octonions Book in PDF, ePub and Kindle
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
Author | : Marilyn M. Simmons |
Publisher | : |
Total Pages | : 104 |
Release | : 1992 |
Genre | : Numbers, Complex |
ISBN | : |
Download Historical Aspects of Complex, Quaternions and Cayley Numbers Book in PDF, ePub and Kindle
Author | : Marlene Tellinghuisen Tate |
Publisher | : |
Total Pages | : 78 |
Release | : 1964 |
Genre | : Algebras, Linear |
ISBN | : |
Download Construction of Quaternions and Cayley Numbers as Examples of Linear Algebras Book in PDF, ePub and Kindle
Author | : Tevian Dray |
Publisher | : World Scientific |
Total Pages | : 229 |
Release | : 2015-04-08 |
Genre | : Mathematics |
ISBN | : 9814401838 |
Download The Geometry Of The Octonions Book in PDF, ePub and Kindle
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.
Author | : Susumu Okubo |
Publisher | : Cambridge University Press |
Total Pages | : 152 |
Release | : 1995-08-03 |
Genre | : Mathematics |
ISBN | : 0521472156 |
Download Introduction to Octonion and Other Non-Associative Algebras in Physics Book in PDF, ePub and Kindle
In this book, the author aims to familiarize researchers and graduate students in both physics and mathematics with the application of non-associative algebras in physics.Topics covered by the author range from algebras of observables in quantum mechanics, angular momentum and octonions, division algebra, triple-linear products and YangSHBaxter equations. The author also covers non-associative gauge theoretic reformulation of Einstein's general relativity theory and so on. Much of the material found in this book is not available in other standard works.
Author | : Alexander McAulay |
Publisher | : Createspace Independent Publishing Platform |
Total Pages | : 120 |
Release | : 2017-06-18 |
Genre | : |
ISBN | : 9781548174828 |
Download Utility of Quaternions in Physics Book in PDF, ePub and Kindle
In math, the quaternions are a number method that extends the complex numbers. They were originally described by the mathematician William Rowan Hamilton and applied to mechanics in space (3D). Quaternions characteristics are that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two lines in 3D (the quotient of two vectors). Quaternions find uses in theoretical and applied mathematics, in particular for calculations involving 3D rotations such as in computer graphics, computer vision, and crystallographic texture analysis. In useful applications, they find use alongside other methods, like Euler angles and rotation matrices, depending on the application. In contemporary mathematical language, quaternions form a 4D associative normed division algebra over the real numbers, and consequently also a domain. In fact, the quaternions were the elementary noncommutative division algebra to be discovered. According to the Frobenius theorem, it is one of only two finite-dimensional dividing rings containing the real numbers as a proper subring, and the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of whichever quaternions are the largest associative algebra.
Author | : Tonny A. Springer |
Publisher | : Springer |
Total Pages | : 212 |
Release | : 2013-12-21 |
Genre | : Mathematics |
ISBN | : 3662126222 |
Download Octonions, Jordan Algebras and Exceptional Groups Book in PDF, ePub and Kindle
The 1963 Göttingen notes of T. A. Springer are well known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra.
Author | : Ron Goldman |
Publisher | : Morgan & Claypool Publishers |
Total Pages | : 177 |
Release | : 2010 |
Genre | : Computers |
ISBN | : 1608454207 |
Download Rethinking Quaternions Book in PDF, ePub and Kindle
In addition to these theoretical issues, we also address some computational questions. We develop straightforward formulas for converting back and forth between quaternion and matrix representations for rotations, reflections, and perspective projections, and we discuss the relative advantages and disadvantages of the quaternion and matrix representations for these transformations. Moreover, we show how to avoid distortions due to floating point computations with rotations by using unit quaternions to represent rotations. We also derive the formula for spherical linear interpolation, and we explain how to apply this formula to interpolate between two rotations for key frame animation. Finally, we explain the role of quaternions in low-dimensional Clifford algebras, and we show how to apply the Clifford algebra for R3 to model rotations, reflections, and perspective projections. To help the reader understand the concepts and formulas presented here, we have incorporated many exercises in order to clarify and elaborate some of the key points in the text."--P. 4 of cover.
Author | : John Horton Conway |
Publisher | : |
Total Pages | : 159 |
Release | : 2005 |
Genre | : |
ISBN | : |
Download On Quaternions and Octonions Book in PDF, ePub and Kindle