Название: Geometric Algebra Applications Vol. III: Integral Transforms, Machine Learning, and Quantum Computing
Автор: Eduardo Bayro-Corrochano
Издательство: Springer
Год: 2024
Страниц: 662
Язык: английский
Формат: pdf (true)
Размер: 36.1 MB
The goal of Geometric Algebra Applications Vol. III: Integral Transforms, Machine Learning, and Quantum Computing is to present a unified mathematical treatment of diverse problems in the general domain like Clifford Fourier Transforms, Deep Learning and Geometric Algebra Convolutional Neural Networks, Quaternion Quantum Fourier Transform and Geometric Quantum Computing. This book presents the theory and applications of an advanced mathematical language called geometric algebra that greatly helps to express ideas and concepts, and to develop algorithms in the broad domain of robot physics. In this book, we present geometric algebra, which we believe is the most powerful available mathematical system to date. It is a unifying language for treating Information Theory, Machine Learning, and Quantum Computing; as a result, the knowledge is not fragmented and we can produce compact and less redundant mathematical expressions that are prone to be optimized for real-time applications. Thorough discussion of several tasks of computer vision, graphics, neurocomputing, and robotics. machine learning, Deep Learning and CNNs, and Geometric Quantum Computing using the geometric algebra framework. 130 exercises and hints for the development of future computer software packages for extensive calculations in geometric algebra. An entire section is dedicated to explaining how one should write the subroutines in C++, Python, Matlab, and Maple to carry out efficient geometric computations in the geometric algebra framework. Furthermore, it is shown how program code can be optimized for real-time computations. The book is an essential resource for applied mathematicians, physicists, computer scientists, graphics engineering, AI and Machine Learning researchers, roboticists and mechanical and electrical engineers, neurocomputing researchers, neuroscientists, and quantum computing specialists.
