Lectures on Quaternions PDF Download

Author: Sir William Rowan Hamilton
Publisher:
ISBN:
Category : Quaternions
Languages : en
Pages : 886

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Author: Sir William Rowan Hamilton
Publisher:
ISBN:
Category : Quaternions
Languages : en
Pages : 1016

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Book Description

Author: Sir William Rowan Hamilton
Publisher:
ISBN:
Category :
Languages : en
Pages : 882

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Book Description

Author: Sir William Rowan Hamilton
Publisher:
ISBN:
Category : Quaternions
Languages : en
Pages : 890

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Author: Ron Goldman
Publisher: Morgan & Claypool Publishers
ISBN: 1608454207
Category : Computers
Languages : en
Pages : 177

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Book Description
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: Ivor Grattan-Guinness
Publisher: Elsevier
ISBN: 0080457444
Category : Mathematics
Languages : en
Pages : 1042

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Book Description
This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. - First book of its kind - Covers the period 1640-1940 of massive development in mathematics - Describes many of the main writings of mathematics - Articles written by specialists in their field

Author: John Voight
Publisher: Springer Nature
ISBN: 3030566943
Category : Mathematics
Languages : en
Pages : 877

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Book Description
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.

Author: International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics
Publisher:
ISBN:
Category : Mathematicians
Languages : en
Pages : 196

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List of members in each number.

Author: International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 512

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Author: A. L. James
Publisher: Taylor & Francis
ISBN: 1040157394
Category : Music
Languages : en
Pages : 172

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Book Description
Ornette Coleman, Psychoanalysis, Discourse develops tools from psychoanalysis for the analysis of Ornette Coleman's discourse. In this psychoanalytic, philosophical and musical meditation on what it means to follow, A. L. James presents an approach to the analysis of discourse that is a kind of listening for listening – an attempt to discern in and between the lines of Coleman's speech the implication of new ways to listen, new ways to experience Coleman’s music as movement and space – as Movements in Harmolodic Space. Each chapter of this book is oriented with respect to fragments from Coleman’s discourse, dealing with a piece, or collection of pieces, from Coleman’s work, with particular attention to the implication of relations and relationality. Insofar as Coleman’s discourse about his work also contains allusions to fields beyond music, it develops tools that draw elements and structures from these fields together, finding in their relation echoes and parallels. Ornette Coleman, Psychoanalysis, Discourse will be of great interest to psychoanalysts, musicians, and musicologists. It will be relevant for academics and scholars of psychoanalytic and Lacanian studies, music, and cultural studies.