Quaternion and Clifford Fourier Transforms and Wavelets

Stephen J. Sangwine

ISBN 10: 3034807775 / ISBN 13: 9783034807777

Edité par Springer Basel, Birkhäuser Basel, 2015

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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. 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. 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.

N° de réf. du vendeur 9783034807777

Détails bibliographiques

• Titre: Quaternion and Clifford Fourier Transforms and Wavelets
• Éditeur: Springer Basel, Birkhäuser Basel
• Date de parution: 2015
• Langue: anglais
• ISBN à 10 chiffres: 3034807775
• ISBN à 13 chiffres: 9783034807777
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 20 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 20 millimètres de profondeur
• Poids: 557 grammes

A propos de ce titre

Synopsis

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.

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.

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.

Présentation de l'éditeur

This book discusses the state of the art of hypercomplex Fourier and Wavelet Transformations, both from the side of theoretical investigations and in the context of applications. Draws attention to matrix isomorphisms for hypercomplex algebras.