Editors:
- First book on this topics combining theory and applications
- Comprehensive overview addressing both mathematicians and engineers
- Provides a representative overview of the relevant literature
Part of the book series: Trends in Mathematics (TM)
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Table of contents (16 chapters)
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Front Matter
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Quaternions
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Front Matter
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Clifford Algebra
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Front Matter
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Back Matter
About this book
Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts.
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This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp.
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It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.
Editors and Affiliations
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, Department of Material Science, International Christian University, Tokyo, Japan
Eckhard Hitzer
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School of Computer Science and, Electronic Engineering, University of Essex, Colchester, United Kingdom
Stephen J. Sangwine
Bibliographic Information
Book Title: Quaternion and Clifford Fourier Transforms and Wavelets
Editors: Eckhard Hitzer, Stephen J. Sangwine
Series Title: Trends in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-0603-9
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2013
Hardcover ISBN: 978-3-0348-0602-2Published: 04 July 2013
Softcover ISBN: 978-3-0348-0777-7Published: 09 July 2015
eBook ISBN: 978-3-0348-0603-9Published: 24 June 2013
Series ISSN: 2297-0215
Series E-ISSN: 2297-024X
Edition Number: 1
Number of Pages: XXVII, 338
Topics: Number Theory, Linear and Multilinear Algebras, Matrix Theory, Numerical Analysis, Fourier Analysis, Image Processing and Computer Vision
Industry Sectors: IT & Software