Linear Algebra And Geometry

Author : Igor R. Shafarevich,Alexey O. Remizov
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 40,6 Mb
Release : 2012-08-23
Category : Mathematics
ISBN : 9783642309946

Get Book

Linear Algebra and Geometry by Igor R. Shafarevich,Alexey O. Remizov Pdf

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

Author : P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin
Publisher : CRC Press
Page : 324 pages
File Size : 41,7 Mb
Release : 1997-10-01
Category : Mathematics
ISBN : 9056990497

Get Book

Linear Algebra and Geometry by P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin Pdf

This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metic, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics.

Author : Bruce Solomon
Publisher : CRC Press
Page : 474 pages
File Size : 51,5 Mb
Release : 2014-12-12
Category : Mathematics
ISBN : 9781482299304

Get Book

Linear Algebra, Geometry and Transformation by Bruce Solomon Pdf

The Essentials of a First Linear Algebra Course and MoreLinear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem.An Engaging Treatment of the Interplay amo

Author : Al Cuoco,Kevin Waterman,Bowen Kerins,Elena Kaczorowski,Michelle Manes
Publisher : American Mathematical Soc.
Page : 557 pages
File Size : 41,6 Mb
Release : 2019-04-10
Category : Algebras, Linear
ISBN : 9781470443504

Get Book

Linear Algebra and Geometry by Al Cuoco,Kevin Waterman,Bowen Kerins,Elena Kaczorowski,Michelle Manes Pdf

Linear Algebra and Geometry is organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field. The materials in Linear Algebra and Geometry have been used, field tested, and refined for over two decades. It is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. Secondary teachers will find the emphasis on developing effective habits of mind especially helpful. The book is written in a friendly, approachable voice and contains nearly a thousand problems. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to [email protected] for more information.

Author : Reinhold Baer
Publisher : Courier Corporation
Page : 338 pages
File Size : 49,5 Mb
Release : 2012-06-11
Category : Mathematics
ISBN : 9780486154664

Get Book

Linear Algebra and Projective Geometry by Reinhold Baer Pdf

Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.

Author : Irving Kaplansky
Publisher : Courier Corporation
Page : 182 pages
File Size : 45,9 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0486432335

Get Book

Linear Algebra and Geometry by Irving Kaplansky Pdf

The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Focusing on inner product spaces, orthogonal similarity, and elements of geometry, this volume is illustrated with an abundance of examples, exercises, and proofs and is suitable for both undergraduate and graduate courses. 1974 edition.

Author : Thomas Banchoff,John Wermer
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461243908

Get Book

Linear Algebra Through Geometry by Thomas Banchoff,John Wermer Pdf

This book introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space.

Author : Giovanni Landi,Alessandro Zampini
Publisher : Springer
Page : 345 pages
File Size : 40,5 Mb
Release : 2018-05-12
Category : Science
ISBN : 9783319783611

Get Book

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 : E. Sernesi
Publisher : Routledge
Page : 274 pages
File Size : 44,8 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351435284

Get Book

Linear Algebra by E. Sernesi Pdf

This is an undergraduate textbook suitable for linear algebra courses. This is the only textbook that develops the linear algebra hand-in-hand with the geometry of linear (or affine) spaces in such a way that the understanding of each reinforces the other. The text is divided into two parts: Part I is on linear algebra and affine geometry, finis

Author : Alexandra I. Kostrikin
Publisher : CRC Press
Page : 480 pages
File Size : 50,8 Mb
Release : 1996-02-09
Category : Mathematics
ISBN : 2884490302

Get Book

Exercises in Algebra by Alexandra I. Kostrikin Pdf

This book is a collection of exercises for courses in higher algebra, linear algebra and geometry. It is helpful for postgraduate students in checking the solutions and answers to the exercises.

Author : Nathaniel Johnston
Publisher : Springer Nature
Page : 482 pages
File Size : 54,6 Mb
Release : 2021-05-19
Category : Mathematics
ISBN : 9783030528119

Get Book

Introduction to Linear and Matrix Algebra by Nathaniel Johnston Pdf

This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

Author : K. W. Gruenberg,A. J. Weir
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 40,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781475741018

Get Book

Linear Geometry by K. W. Gruenberg,A. J. Weir Pdf

This is essentially a book on linear algebra. But the approach is somewhat unusual in that we emphasise throughout the geometric aspect of the subject. The material is suitable for a course on linear algebra for mathe matics majors at North American Universities in their junior or senior year and at British Universities in their second or third year. However, in view of the structure of undergraduate courses in the United States, it is very possible that, at many institutions, the text may be found more suitable at the beginning graduate level. The book has two aims: to provide a basic course in linear algebra up to, and including, modules over a principal ideal domain; and to explain in rigorous language the intuitively familiar concepts of euclidean, affine, and projective geometry and the relations between them. It is increasingly recognised that linear algebra should be approached from a geometric point of VIew. This applies not only to mathematics majors but also to mathematically-oriented natural scientists and engineers.

Author : David M. Bloom
Publisher : CUP Archive
Page : 652 pages
File Size : 46,6 Mb
Release : 1979-06-29
Category : Mathematics
ISBN : 0521293243

Get Book

Linear Algebra and Geometry by David M. Bloom Pdf

Author : Kam-Tim Leung
Publisher : Hong Kong University Press
Page : 320 pages
File Size : 45,5 Mb
Release : 1974-01-01
Category : Mathematics
ISBN : 9780856561115

Get Book

Linear Algebra and Geometry by Kam-Tim Leung Pdf

Linear algebra is now included in the undergraduate curriculum of most universities. It is generally recognized that this branch of algebra, being less abstract and directly motivated by geometry, is easier to understand than some other branches and that because of the wide applications it should be taught as soon as possible. This book is an extension of the lecture notes for a course in algebra and geometry for first-year undergraduates of mathematics and physical sciences. Except for some rudimentary knowledge in the language of set theory the prerequisites for using the main part of the book do not go beyond form VI level. Since it is intended for use by beginners, much care is taken to explain new theories by building up from intuitive ideas and by many illustrative examples, though the general level of presentation is thoroughly axiomatic. Another feature of the book for the more capable students is the introduction of the language and ideas of category theory through which a deeper understanding of linear algebra can be achieved.

Author : S. KUMARESAN
Publisher : PHI Learning Pvt. Ltd.
Page : 240 pages
File Size : 43,7 Mb
Release : 2000-01-01
Category : Mathematics
ISBN : 9788120316287

Get Book

LINEAR ALGEBRA by S. KUMARESAN Pdf

This clear, concise and highly readable text is designed for a first course in linear algebra and is intended for undergraduate courses in mathematics. It focusses throughout on geometric explanations to make the student perceive that linear algebra is nothing but analytic geometry of n dimensions. From the very start, linear algebra is presented as an extension of the theory of simultaneous linear equations and their geometric interpretation is shown to be a recurring theme of the subject. The integration of abstract algebraic concepts with the underlying geometric notions is one of the most distinguishing features of this book — designed to help students in the pursuit of multivariable calculus and differential geometry in subsequent courses.Explanations and concepts are logically presented in a conversational tone and well-constructed writing style so that students at a variety of levels can understand the material and acquire a solid foundation in the basic skills of linear algebra.