By Jim Byrnes, Gerald Ostheimer

The fusion of algebra, research and geometry, and their software to genuine international difficulties, were dominant subject matters underlying arithmetic for over a century. Geometric algebras, brought and categorized through Clifford within the overdue nineteenth century, have performed a sought after function during this attempt, as obvious within the mathematical paintings of Cartan, Brauer, Weyl, Chevelley, Atiyah, and Bott, and in purposes to physics within the paintings of Pauli, Dirac and others. probably the most vital functions of geometric algebras to geometry is to the illustration of teams of Euclidean and Minkowski rotations. This point and its direct relation to robotics and imaginative and prescient may be mentioned in numerous chapters of this multi-authored textbook, which resulted from the ASI meeting.

Moreover, staff conception, starting with the paintings of Burnside, Frobenius and Schur, has been prompted via much more basic difficulties. for this reason, normal team activities have supplied the atmosphere for strong tools inside of team concept and for using teams in purposes to physics, chemistry, molecular biology, and sign processing. those facets, too, might be coated in detail.

With the speedily starting to be significance of, and ever increasing conceptual and computational calls for on sign and picture processing in distant sensing, laptop imaginative and prescient, scientific picture processing, and organic sign processing, and on neural and quantum computing, geometric algebras, and computational workforce harmonic research, the subjects of the ebook have emerged as key instruments. The checklist of authors comprises a few of the world's prime specialists within the improvement of latest algebraic modeling and sign illustration methodologies, novel Fourier-based and geometric transforms, and computational algorithms required for figuring out the opportunity of those new software fields.

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