Abstract Algebra Vector Spaces
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Groups Matrices And Vector Spaces
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Author : James B. Carrell
language : en
Publisher: Springer
Release Date : 2017-09-02
Groups Matrices And Vector Spaces written by James B. Carrell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-02 with Mathematics categories.
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.
Rings Fields And Vector Spaces
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Author : Bharath Sethuraman
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-11-26
Rings Fields And Vector Spaces written by Bharath Sethuraman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-26 with Mathematics categories.
Using the proof of the non-trisectability of an arbitrary angle as a final goal, the author develops in an easy conversational style the basics of rings, fields, and vector spaces. Originally developed as a text for an introduction to algebra course for future high-school teachers at California State University, Northridge, the focus of this book is on exposition. It would serve extremely well as a focused, one-semester introduction to abstract algebra.
Linear Algebra As An Introduction To Abstract Mathematics
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Author : Bruno Nachtergaele
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-11-30
Linear Algebra As An Introduction To Abstract Mathematics written by Bruno Nachtergaele and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-30 with Mathematics categories.
This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.
Abstract Algebra Vector Spaces
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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :
Abstract Algebra Vector Spaces written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"Abstract Algebra: Vector Spaces" is a comprehensive exploration of vector spaces within the realm of abstract algebra, offering a clear and insightful journey into foundational concepts and their diverse applications. From fundamental definitions of basis and dimension to advanced topics like quantum mechanics, coding theory, and data science, this book equips readers with a robust understanding of how vector spaces underpin various theoretical frameworks and real-world problems. With an emphasis on clarity and practical relevance, it serves as an invaluable resource for students, researchers, and enthusiasts seeking to deepen their knowledge and explore the profound connections between algebraic structures and modern applications.
A Course In Linear Algebra With Applications
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Author : Derek John Scott Robinson
language : en
Publisher: World Scientific
Release Date : 1991
A Course In Linear Algebra With Applications written by Derek John Scott Robinson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This solution booklet is a supplement to the book "A Course in Linear Algebra with Applications". It will be useful to lecturers and to students taking the subject since it contains complete solutions to all 283 exercises in the book.
Linear Algebra Done Right
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Author : Sheldon Axler
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-18
Linear Algebra Done Right written by Sheldon Axler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-18 with Mathematics categories.
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Basic Matrix Theory
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Author : Leonard E. Fuller
language : en
Publisher: Courier Dover Publications
Release Date : 2017-09-13
Basic Matrix Theory written by Leonard E. Fuller and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-13 with Mathematics categories.
This guide to using matrices as a mathematical tool offers a model for procedure rather than an exposition of theory. Detailed examples illustrate the focus on computational methods. 1962 edition.
Introduction To Applied Linear Algebra
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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07
Introduction To Applied Linear Algebra written by Stephen Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Business & Economics categories.
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Applied Linear Algebra
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Author : Peter J. Olver
language : en
Publisher: Springer
Release Date : 2018-05-30
Applied Linear Algebra written by Peter J. Olver and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-30 with Mathematics categories.
This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.
Linear Algebra Problem Book
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Author : Paul R. Halmos
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-12-31
Linear Algebra Problem Book written by Paul R. Halmos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-31 with Mathematics categories.
Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.