Matrix and Tensor Calculas

This book presents the algorithms used to provide recommendations by exploiting matrix factorization and tensor decomposition techniques. It highlights well-known decomposition methods for recommender

This book provides comprehensive reviews of recent progress in matrix variate and tensor variate data analysis from applied points of view. Matrix and tensor approaches for data analysis are known to

This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF). This includes NMF’s various extensions and modifications, especially Nonnegative

This balanced and comprehensive study presents the theory, methods and applications of matrix analysis in a new theoretical framework, allowing readers to understand second-order and higher-order matrix analysis in a completely new light. Alongside the core subjects in matrix analysis, such as singular value analysis, the solution of matrix equations and eigenanalysis, the author introduces new applications and perspectives that are unique to this book. The very topical subjects of gradient analysis and optimization play a central role here. Also included are subspace analysis, projection analysis and tensor analysis, subjects which are often neglected in other books. Having provided a solid foundation to the subject, the author goes on to place particular emphasis on the many applications matrix analysis has in science and engineering, making this book suitable for scientists, engineers and graduate students alike.

This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of pote

This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of pote

This rigorous and advanced mathematical explanation of classic tensor analysis was written by one of the founders of tensor calculus. Its concise exposition of the mathematical basis of the discipline is integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity, and Dirac's matrix calculus. 1954 edition.

A generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP.

This volume offers a working knowledge of the fundamentals of matrix and tensor calculus that can be applied to a variety of fields, particularly scientific aeronautical engineering. Mathematicians, p

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Group theory helps readers in understanding the energy spectrum and the degeneracy of systems possessing discrete symmetry and continuous symmetry. The fundamental concepts of group theory and its applications are presented with the help of solved problems and exercises. The text covers two essential aspects of group theory, namely discrete groups and Lie groups. Important concepts including permutation groups, point groups and irreducible representation related to discrete groups are discussed with the aid of solved problems. Topics such as the matrix exponential, the circle group, tensor products, angular momentum algebra and the Lorentz group are explained to help readers in understanding the quark model and theory composites. Real-life applications including molecular vibration, level splitting perturbation, crystal field splitting and the orthogonal group are also covered. Application-oriented solved problems and exercises are interspersed throughout the text to reinforce understa

Molecular Rydberg states have many unusual properties, lending themselves to a diverse range of experimental applications. This book is designed to unravel the mysteries of molecular Rydberg states that lie beyond the scope of accepted spectroscopic theories. It is the first single-authored text to focus on the application of multi-channel quantum defect theory (MQDT) and ab initio theory to this special class of molecular systems, introducing readers to novel theoretical techniques. The scattering techniques of MQDT are examined, along with a unified description of bound states and fragmentation dynamics. Connections with established spectroscopic theory are also described. The book concludes with an account of the spherical tensor and density matrix theories required for the interpretation of multi-photon experiments. While the main text focuses on physical principles and experimental applications, appendices are used to handle advanced mathematical detail. This is a valuable resourc

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly fr

Group theory helps readers in understanding the energy spectrum and the degeneracy of systems possessing discrete symmetry and continuous symmetry. The fundamental concepts of group theory and its applications are presented with the help of solved problems and exercises. The text covers two essential aspects of group theory, namely discrete groups and Lie groups. Important concepts including permutation groups, point groups and irreducible representation related to discrete groups are discussed with the aid of solved problems. Topics such as the matrix exponential, the circle group, tensor products, angular momentum algebra and the Lorentz group are explained to help readers in understanding the quark model and theory composites. Real-life applications including molecular vibration, level splitting perturbation, crystal field splitting and the orthogonal group are also covered. Application-oriented solved problems and exercises are interspersed throughout the text to reinforce understa