Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Clifford algebras. --- Fourier analysis. --- Quaternions. --- Wavelets (Mathematics). --- Quaternions --- Clifford algebras --- Fourier analysis --- Wavelets (Mathematics) --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Fourier transformations. --- Wavelet analysis --- Transformations, Fourier --- Transforms, Fourier --- Mathematics. --- Image processing. --- Matrix theory. --- Algebra. --- Numerical analysis. --- Number theory. --- Number Theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Numerical Analysis. --- Fourier Analysis. --- Image Processing and Computer Vision. --- Harmonic analysis --- Transformations (Mathematics) --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Analysis, Fourier --- Mathematical analysis --- Number study --- Numbers, Theory of --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment