Vector Spaces And Matrices In Physics

Author : M. C. Jain
Publisher : CRC Press
Page : 184 pages
File Size : 45,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0849309786

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Vector Spaces and Matrices in Physics by M. C. Jain Pdf

The theory of vector spaces and matrices is an essential part of the mathematical background required by physicists. Most books on the subject, however, do not adequately meet the requirements of physics courses-they tend to be either highly mathematical or too elementary. Books that focus on mathematical theory may render the subject too dry to hold the interest of physics students, while books that are more elementary tend to neglect some topics that are vital in the development of physical theories. In particular, there is often very little discussion of vector spaces, and many books introduce matrices merely as a computational tool. Vector Spaces and Matrices in Physics fills the gap between the elementary and the heavily mathematical treatments of the subject with an approach and presentation ideal for graduate-level physics students. After building a foundation in vector spaces and matrix algebra, the author takes care to emphasize the role of matrices as representations of linear transformations on vector spaces, a concept of matrix theory that is essential for a proper understanding of quantum mechanics. He includes numerous solved and unsolved problems, and enough hints for the unsolved problems to make the book self-sufficient. Developed through many years of lecture notes, Vector Spaces and Matrices in Physics was written primarily as a graduate and post-graduate textbook and as a reference for physicists. Its clear presentation and concise but thorough coverage, however, make it useful for engineers, chemists, economists, and anyone who needs a background in matrices for application in other areas.

Author : Sharma,Sharma Vinod K.
Publisher : PHI Learning Pvt. Ltd.
Page : 498 pages
File Size : 49,5 Mb
Release : 2009-12
Category : Science
ISBN : 9788120338661

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Matrix Methods and Vector Spaces in Physics by Sharma,Sharma Vinod K. Pdf

They have wide applications in a number of subjects ranging from solid state physics, solid/fluid mechanics to relativity and electromagnetics. This well-written book gives, in an easy-to-read style, a step-by-step and comprehensive understanding about the various concepts, theories and applications of vector spaces, matrices and tensors. The book equips the reader with the fundamental knowledge in such subjects as matrix theory, linear algebraic equations, applications of eigenvalues and eigenvectors, diagonalisation process, quadratic forms, Cartesian tensors and more.

Author : M. C. Jain
Publisher : Unknown
Page : 284 pages
File Size : 53,9 Mb
Release : 2018-04-30
Category : Technology & Engineering
ISBN : 1783323760

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Vector Spaces, Matrices and Tensors in Physics by M. C. Jain Pdf

Vector spaces, matrices, and tensors in physics form an essential part of the mathematical background required by physicists. This book is written primarily as textbook for undergraduate and postgraduate students and as a reference book for working physicists. Special emphasis is given to topics relevant to physics, for example linear independence and dependence of vectors, inner product, orthonormality, matrices as representations of linear transformations on vector spaces, similarity, eigenvalues, eigenvectors, diagonalization of matrices, expressing various physical quantities as tensors, tensorial formulation of vector algebra, calculus and geometry. The role of orthogonal, hermitian and unitary matrices in physics is highlighted.

Author : Robert M. Thrall,Leonard Tornheim
Publisher : Courier Corporation
Page : 336 pages
File Size : 47,9 Mb
Release : 2014-01-15
Category : Mathematics
ISBN : 9780486321059

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Vector Spaces and Matrices by Robert M. Thrall,Leonard Tornheim Pdf

Students receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. Suitable as a primary or supplementary text for college-level courses in linear algebra. 1957 edition.

Author : A. W. Joshi
Publisher : New Age International
Page : 364 pages
File Size : 41,6 Mb
Release : 1995
Category : Mathematics
ISBN : 8122405630

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Matrices and Tensors in Physics by A. W. Joshi Pdf

The First Part Of This Book Begins With An Introduction To Matrices Through Linear Transformations On Vector Spaces, Followed By A Discussion On The Algebra Of Matrices, Special Matrices, Linear Equations, The Eigenvalue Problem, Bilinear And Quadratic Forms, Kronecker Sum And Product Of Matrices. Other Matrices Which Occur In Physics, Such As The Rotation Matrix, Pauli Spin Matrices And Dirac Matrices, Are Then Presented. A Brief Account Of Infinite Matrices From The Point Of View Of Matrix Formulation Of Quantum Mechanics Is Also Included. The Emphasis In This Part Is On Linear Dependence And Independence Of Vectors And Matrices, Linear Combinations, Independent Parameters Of Various Special Matrices And Such Other Concepts As Help The Student In Obtaining A Clear Understanding Of The Subject. A Simplified Proof Of The Theorem That A Common Set Of Eigenvectors Can Be Found For Two Commuting Matrices Is Given. The Second Part Deals With Cartesian And General Tensors. Many Physical Situations Are Discussed Which Require The Use Of Second And Higher Rank Tensors, Such As Effective Mass Tensor, Moment Of Inertia Tensor, Stress, Strain And Elastic Constants, Piezoelectric Strain Coefficient Tensor, Etc. Einsteins Summation Convention Is Explained In Detail And Common Errors Arising In Its Use Are Pointed Out. Rules For Checking The Correctness Of Tensor Equations Are Given. This Is Followed By Four-Vectors In Special Relativity And Covarient Formulation Of Electrodynamics. This Part Comes To An End With The Concept Of Parallel Displacement Of Vectors In Riemannian Space And Covariant Derivative Of Tensors, Leading To The Curvature Tensors And Its Properties.Appendix I Has Expanded And Two New Appendices Have Been Added In This Edition.

Author : K. A. I. L. Wijewardena Gamalath
Publisher : Cambridge India
Page : 244 pages
File Size : 40,8 Mb
Release : 2007-03
Category : Science
ISBN : 9788175964365

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Introduction to Vector Spaces in Physics by K. A. I. L. Wijewardena Gamalath Pdf

Introduction to Fourier Transforms in Physics

Author : James B. Carrell
Publisher : Springer
Page : 410 pages
File Size : 46,9 Mb
Release : 2017-09-02
Category : Mathematics
ISBN : 9780387794280

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Groups, Matrices, and Vector Spaces by James B. Carrell Pdf

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 : Lawrence P. Huelsman
Publisher : Courier Corporation
Page : 304 pages
File Size : 40,5 Mb
Release : 2013-08-16
Category : Technology & Engineering
ISBN : 9780486280448

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Circuits, Matrices and Linear Vector Spaces by Lawrence P. Huelsman Pdf

This high-level text explains the mathematics behind basic circuit theory. It covers matrix algebra, the basic theory of n-dimensional spaces, and applications to linear systems. Numerous problems. 1963 edition.

Author : Mustafa A. Akcoglu,Paul F. A. Bartha,Dzung Minh Ha
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 42,7 Mb
Release : 2011-09-09
Category : Mathematics
ISBN : 9781118164594

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Analysis in Vector Spaces by Mustafa A. Akcoglu,Paul F. A. Bartha,Dzung Minh Ha Pdf

A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined withrelated computational methods are essential to understanding nearlyall areas of quantitative science. Analysis in Vector Spacespresents the central results of this classic subject throughrigorous arguments, discussions, and examples. The book aims tocultivate not only knowledge of the major theoretical results, butalso the geometric intuition needed for both mathematicalproblem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology,and notation and also provide a basic introduction to set theory,the properties of real numbers, and a review of linear algebra. Anelegant approach to eigenvector problems and the spectral theoremsets the stage for later results on volume and integration.Subsequent chapters present the major results of differential andintegral calculus of several variables as well as the theory ofmanifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter toreinforce new concepts and to illustrate how results can be appliedto additional problems. Furthermore, proofs and examples arepresented in a clear style that emphasizes the underlying intuitiveideas. Counterexamples are provided throughout the book to warnagainst possible mistakes, and extensive appendices outline theconstruction of real numbers, include a fundamental result aboutdimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra andsingle variable calculus, Analysis in Vector Spaces is anexcellent book for a second course in analysis for mathematics,physics, computer science, and engineering majors at theundergraduate and graduate levels. It also serves as a valuablereference for further study in any discipline that requires a firmunderstanding of mathematical techniques and concepts.

Author : Palash B. Pal
Publisher : Cambridge University Press
Page : 717 pages
File Size : 51,5 Mb
Release : 2019-05-23
Category : Science
ISBN : 9781108492201

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A Physicists Introduction to Algebraic Structures by Palash B. Pal Pdf

Algebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections.

Author : Giovanni Landi,Alessandro Zampini
Publisher : Springer
Page : 345 pages
File Size : 40,6 Mb
Release : 2018-05-12
Category : Science
ISBN : 9783319783611

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Linear Algebra and Analytic Geometry for Physical Sciences by Giovanni Landi,Alessandro Zampini Pdf

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises.Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number.The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.

Author : F. Brickell
Publisher : Unknown
Page : 128 pages
File Size : 52,8 Mb
Release : 1972-01-01
Category : Electronic
ISBN : 0844809470

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Matrices and Vector Spaces by F. Brickell Pdf

Author : Robert B. Scott
Publisher : Springer Nature
Page : 188 pages
File Size : 40,5 Mb
Release : 2023-08-09
Category : Science
ISBN : 9783031312182

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Problems and Solutions on Vector Spaces for Physicists by Robert B. Scott Pdf

This book offers supporting material for the comprehensive textbook Mathematical Physics—A Modern Introduction to Its Foundations authored by Sadri Hassani. The book covers mathematical preliminaries and all of Part I in Hassani’s textbook. The subjects covered here include the key topics necessary for physicists to form a solid mathematical foundation: vectors and linear maps, algebras, operators, matrices, and spectral decomposition. In particular, the vector space concept is a central unifying theme in later chapters of Hassani’s textbook. Detailed solutions are provided to one third of the end-of-chapter exercises in the first six chapters of his text. The present volume helps upper-undergraduate and early postgraduate physics students deepen their understanding of the mathematics that they encounter in physics, learn physics more efficiently, and use mathematics with more confidence and creativity. The content is thus presented rigorously but remains accessible to physics students. New exercises are also proposed, some with solutions, some without, so that the total number of unsolved exercises remains unchanged. They are chosen to help explain difficult concepts, amplify key points in Hassani's textbook, or make further connections with applications in physics. Taken together with Hassani's work, the two form a self-contained set and the solutions make detailed reference to Hassani's text. The solutions also refer to other mathematics and physics textbooks, providing entry points to further literature that finds a useful place in the physicist's personal library.

Author : Jacob T. Schwartz
Publisher : Courier Corporation
Page : 198 pages
File Size : 49,6 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486143705

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Introduction to Matrices and Vectors by Jacob T. Schwartz Pdf

Realizing that matrices can be a confusing topic for the beginner, the author of this undergraduate text has made things as clear as possible by focusing on problem solving, rather than elaborate proofs. He begins with the basics, offering students a solid foundation for the later chapters on using special matrices to solve problems.The first three chapters present the basics of matrices, including addition, multiplication, and division, and give solid practice in the areas of matrix manipulation where the laws of algebra do not apply. In later chapters the author introduces vectors and shows how to use vectors and matrices to solve systems of linear equations. He also covers special matrices — including complex numbers, quaternion matrices, and matrices with complex entries — and transpose matrices; the trace of a matrix; the cross product of matrices; eigenvalues and eigenvectors; and infinite series of matrices. Exercises at the end of each section give students further practice in problem solving. Prerequisites include a background in algebra, and in the later chapters, a knowledge of solid geometry. The book was designed as an introductory text for college freshmen and sophomores, but selected chapters can also be used to supplement advanced high school classes. Professionals who need a better understanding or review of the subject will also benefit from this concise guide.

Author : Arak M. Mathai,Hans J. Haubold
Publisher : Walter de Gruyter GmbH & Co KG
Page : 670 pages
File Size : 53,5 Mb
Release : 2017-10-23
Category : Mathematics
ISBN : 9783110562590

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Linear Algebra by Arak M. Mathai,Hans J. Haubold Pdf

In order not to intimidate students by a too abstract approach, this textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on statements such as theorems and proofs too much. It is also designed to be self-contained, so no other material is required for an understanding of the topics covered. As the basis for courses on space and atmospheric science, remote sensing, geographic information systems, meteorology, climate and satellite communications at UN-affiliated regional centers, various applications of the formal theory are discussed as well. These include differential equations, statistics, optimization and some engineering-motivated problems in physics. Contents Vectors Matrices Determinants Eigenvalues and eigenvectors Some applications of matrices and determinants Matrix series and additional properties of matrices