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Numerical Range
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more ...
Linear Algebra with Applications
Contributed articles.
Applied and Computational Matrix Analysis
This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.
Operator Theory, Operator Algebras, and Matrix Theory
This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.
Innovations in Multivariate Statistical Analysis
The three decades which have followed the publication of Heinz Neudecker's seminal paper `Some Theorems on Matrix Differentiation with Special Reference to Kronecker Products' in the Journal of the American Statistical Association (1969) have witnessed the growing influence of matrix analysis in many scientific disciplines. Amongst these are the disciplines to which Neudecker has contributed directly - namely econometrics, economics, psychometrics and multivariate analysis. This book aims to illustrate how powerful the tools of matrix analysis have become as weapons in the statistician's armoury. The majority of its chapters are concerned primarily with theoretical innovations, but all of th...
Trends and Perspectives in Linear Statistical Inference
This volume features selected contributions on a variety of topics related to linear statistical inference. The peer-reviewed papers from the International Conference on Trends and Perspectives in Linear Statistical Inference (LinStat 2016) held in Istanbul, Turkey, 22-25 August 2016, cover topics in both theoretical and applied statistics, such as linear models, high-dimensional statistics, computational statistics, the design of experiments, and multivariate analysis. The book is intended for statisticians, Ph.D. students, and professionals who are interested in statistical inference.
Analysis of Complex Networks
Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. This book follows a new approach of including graph theory from a mathematical perspective with specific applications of graph theory in biomedical and computational sciences. The book is written by renowned experts in the field and offers valuable background information for a wide audience.
Mathematical Reviews
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Non-Hermitian Hamiltonians in Quantum Physics
This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.
