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Author : David J. Healy
Publisher :
ISBN 13 : 9780299058517
Total Pages : 0 pages
Book Rating : 4.0/5 (585 download)
Download or read book U.S. Expansionism: The matrices written by David J. Healy and published by . This book was released on 1970 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tõnu Kollo
Publisher : Springer Science & Business Media
ISBN 13 : 1402034199
Total Pages : 490 pages
Book Rating : 4.4/5 (2 download)
Download or read book Advanced Multivariate Statistics with Matrices written by Tõnu Kollo and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The book has been written for graduate students and statis- cians who are not afraid of matrix formalism. The goal is to provide them with a powerful toolkit for their research and to give necessary background and deeper knowledge for further studies in di?erent areas of multivariate statistics. It can also be useful for researchers in applied mathematics and for people working on data analysis and data mining who can ?nd useful methods and ideas for solving their problems. Ithasbeendesignedasatextbookforatwosemestergraduatecourseonmultiva- ate statistics. Such a course has been held at the Swedish Agricultural University in 2001/02. On the other hand, it can be used as material for series of shorter courses. In fact, Chapters 1 and 2 have been used for a graduate course ”Matrices in Statistics” at University of Tartu for the last few years, and Chapters 2 and 3 formed the material for the graduate course ”Multivariate Asymptotic Statistics” in spring 2002. An advanced course ”Multivariate Linear Models” may be based on Chapter 4. A lot of literature is available on multivariate statistical analysis written for di?- ent purposes and for people with di?erent interests, background and knowledge.
Download or read book United States Census of Agriculture, 1964 written by and published by . This book was released on 1967 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter William Champoux
Publisher : Gaia Matrix
ISBN 13 : 0967232805
Total Pages : 268 pages
Book Rating : 4.9/5 (672 download)
Download or read book Gaia Matrix written by Peter William Champoux and published by Gaia Matrix. This book was released on 1999 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jose Jorge Gil Perez
Publisher : CRC Press
ISBN 13 : 1315355256
Total Pages : 248 pages
Book Rating : 4.3/5 (153 download)
Download or read book Polarized Light and the Mueller Matrix Approach written by Jose Jorge Gil Perez and published by CRC Press. This book was released on 2017-07-12 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Up-to-Date Compendium on the Physics and Mathematics of Polarization Phenomena Polarized Light and the Mueller Matrix Approach thoroughly and cohesively integrates basic concepts of polarization phenomena from the dual viewpoints of the states of polarization of electromagnetic waves and the transformations of these states by the action of material media. Through selected examples, it also illustrates actual and potential applications in materials science, biology, and optics technology. The book begins with the basic concepts related to two- and three-dimensional polarization states. It next describes the nondepolarizing linear transformations of the states of polarization through the Jones and Mueller–Jones approaches. The authors then discuss the forms and properties of the Jones and Mueller matrices associated with different types of nondepolarizing media, address the foundations of the Mueller matrix, and delve more deeply into the analysis of the physical parameters associated with Mueller matrices. The authors proceed to interpret arbitrary decomposition and other interesting parallel decompositions as well as compare the powerful serial decompositions of depolarizing Mueller matrix M. They also analyze the general formalism and specific algebraic quantities and notions related to the concept of differential Mueller matrix. The book concludes with useful approaches that provide a geometric point of view on the polarization effects exhibited by different types of media. Suitable for novices and more seasoned professionals, this book covers the main aspects of polarized radiation and polarization effects of material media. It expertly combines physical and mathematical concepts with important approaches for representing media through equivalent systems composed of simple components.
Author : Tuncay Aktosun
Publisher : Springer Nature
ISBN 13 : 3030384314
Total Pages : 631 pages
Book Rating : 4.0/5 (33 download)
Download or read book Direct and Inverse Scattering for the Matrix Schrödinger Equation written by Tuncay Aktosun and published by Springer Nature. This book was released on 2020-05-19 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.
Author : Holmfridur Sigridar Hannesdottir
Publisher : Springer Nature
ISBN 13 : 3031182588
Total Pages : 165 pages
Book Rating : 4.0/5 (311 download)
Download or read book What is the iε for the S-matrix? written by Holmfridur Sigridar Hannesdottir and published by Springer Nature. This book was released on 2023-01-01 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern perspective on the analytic structure of scattering amplitudes in quantum field theory, with the goal of understanding and exploiting consequences of unitarity, causality, and locality. It focuses on the question: Can the S-matrix be complexified in a way consistent with causality? The affirmative answer has been well understood since the 1960s, in the case of 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε-like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties of the physical amplitude. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. We illustrate all the points on explicit examples, both symbolically and numerically, in addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view. To help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points. This book is well suited for anyone with knowledge of quantum field theory at a graduate level who wants to become familiar with the complex-analytic structure of Feynman integrals.
Author : James B. Carrell
Publisher : Springer
ISBN 13 : 038779428X
Total Pages : 410 pages
Book Rating : 4.3/5 (877 download)
Download or read book Groups, Matrices, and Vector Spaces written by James B. Carrell and published by Springer. This book was released on 2017-09-02 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.
Author : Young Suh Kim
Publisher : MDPI
ISBN 13 : 3038425001
Total Pages : 369 pages
Book Rating : 4.0/5 (384 download)
Download or read book Harmonic Oscillators and Two-By-Two Matrices in Symmetry Problems in Physics written by Young Suh Kim and published by MDPI. This book was released on 2018-07-09 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Harmonic Oscillators In Modern Physics" that was published in Symmetry
Author : I. Gohberg
Publisher : Birkhäuser
ISBN 13 : 3034885326
Total Pages : 241 pages
Book Rating : 4.0/5 (348 download)
Download or read book Matrix and Operator Valued Functions written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers on different aspects of operator theory and complex analysis, covering the recent achievements of the Odessa-Kharkov school, where Potapov was very active. The book appeals to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.
Author : James E. Gentle
Publisher : Springer
ISBN 13 : 3319648675
Total Pages : 648 pages
Book Rating : 4.3/5 (196 download)
Download or read book Matrix Algebra written by James E. Gentle and published by Springer. This book was released on 2017-10-12 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Author : Robert A. Liebler
Publisher : CRC Press
ISBN 13 : 0429852878
Total Pages : 260 pages
Book Rating : 4.4/5 (298 download)
Download or read book Basic Matrix Algebra with Algorithms and Applications written by Robert A. Liebler and published by CRC Press. This book was released on 2018-10-03 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear prose, tight organization, and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources, the social sciences, business, or any discipline that eventually requires an understanding of linear models. With extreme pedagogical clarity that avoids abstraction wherever possible, the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials, including test preparation Maple worksheets, are available for download from the Internet. This unassuming but insightful and remarkably original treatment is organized into bite-sized, clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success, it prepares readers well for the more advanced studies their fields ultimately will require.
Author : Lars Elden
Publisher : SIAM
ISBN 13 : 0898716268
Total Pages : 226 pages
Book Rating : 4.8/5 (987 download)
Download or read book Matrix Methods in Data Mining and Pattern Recognition written by Lars Elden and published by SIAM. This book was released on 2007-07-12 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.
Author : Philip George Burke
Publisher : Springer Science & Business Media
ISBN 13 : 3642159311
Total Pages : 746 pages
Book Rating : 4.6/5 (421 download)
Download or read book R-Matrix Theory of Atomic Collisions written by Philip George Burke and published by Springer Science & Business Media. This book was released on 2011-03-28 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commencing with a self-contained overview of atomic collision theory, this monograph presents recent developments of R-matrix theory and its applications to a wide-range of atomic molecular and optical processes. These developments include the electron and photon collisions with atoms, ions and molecules which are required in the analysis of laboratory and astrophysical plasmas, multiphoton processes required in the analysis of superintense laser interactions with atoms and molecules and positron collisions with atoms and molecules required in antimatter studies of scientific and technologial importance. Basic mathematical results and general and widely used R-matrix computer programs are summarized in the appendices.
Author : Abdulaziz D. Alhaidari
Publisher : Springer Science & Business Media
ISBN 13 : 1402060734
Total Pages : 356 pages
Book Rating : 4.4/5 (2 download)
Download or read book The J-Matrix Method written by Abdulaziz D. Alhaidari and published by Springer Science & Business Media. This book was released on 2008-03-20 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although introduced30 years ago, the J-matrix method has witnessed a resurgence of interest in the last few years. In fact, the interest never ceased, as some authors have found in this method an effective way of handling the continuous spectrum of scattering operators, in addition to other operators. The motivation behind the introduction of the J-matrix method will be presented in brief. The introduction of fast computing machines enabled theorists to perform cal- lations, although approximate, in a conveniently short period of time. This made it possible to study varied scenarios and models, and the effects that different possible parameters have on the ?nal results of such calculations. The ?rst area of research that bene?ted from this opportunity was the structural calculation of atomic and nuclear systems. The Hamiltonian element of the system was set up as a matrix in a convenient, ?nite, bound-state-like basis. A matrix of larger size resulted in a better con?guration interaction matrix that was subsequently diagonalized. The discrete energy eigenvalues thus obtained approximated the spectrum of the system, while the eigenfunctions approximated the wave function of the resulting discrete state. Structural theorists were delighted because they were able to obtain very accurate values for the lowest energy states of interest.
Author : T. Kim
Publisher : Elsevier Inc. Chapters
ISBN 13 : 0128090111
Total Pages : 350 pages
Book Rating : 4.1/5 (28 download)
Download or read book Brittle Matrix Composites written by T. Kim and published by Elsevier Inc. Chapters. This book was released on 2012-11-12 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents the results of the investigation of the chemistry of pore solutions of mortars containing both reactive and non-reactive aggregate. The effects of lithium ions (Li+) on chemical compositions of the pore solutions were also explored. In order to accelerate the A SR, all experiments were performed at 55°C. The compositions of the pore solution were measured at short intervals for the period of up to 120 days. The results showed clear difference between the composition of the pore solution of the mortar with non-reactive aggregate (control mortar) and the mortar containing reactive aggregate. The concentrations of Na+, K+ and OH- ions in the reactive systems without Li+ ions continuously decreased until they reached certain threshold level at which point they stabilized. The time of the stabilization of chemistry of pore solution in the reactive systems coincided with the time of the ultimate expansion of mortar bars of the same composition. When LiNO3 was added as a source of Li+ ions, the consumption of Na+ and K+ ions was significantly reduced. However, the concentrations of Li+ and OH- ions in the pore solution decreased over time.
Author : Édouard Brezin
Publisher : Springer Science & Business Media
ISBN 13 : 9781402045301
Total Pages : 528 pages
Book Rating : 4.0/5 (453 download)
Download or read book Applications of Random Matrices in Physics written by Édouard Brezin and published by Springer Science & Business Media. This book was released on 2006-03-03 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute on Applications of Random Matrices in Physics, Les Houches, France, 6-25 June 2004
