Vectors, Matrices and Geometry

Author: K.T. Leung,S.N. Suen

Publisher: Hong Kong University Press

ISBN: 9622093604

Category: Mathematics

Page: 356

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This book is the last volume of a three-book series written for Sixth Form students and first-year undergraduates. It introduces the important concepts of finite-dimensional vector spaces through the careful study of Euclidean geometry. In turn, methods of linear algebra are then used in the study of coordinate transformations through which a complete classification of conic sections and quadric surfaces is obtained. The book concludes with a detailed treatment of linear equations in n variables in the language of vectors and matrices. Illustrative examples are included in the main text and numerous exercises are given in each section. The other books in the series are Fundamental Concepts of Mathematics (published 1988) and Polynomials and Equations (published 1992).

Vectors and Matrices

Author: Pamela Liebeck

Publisher: Elsevier

ISBN: 1483280438

Category: Mathematics

Page: 192

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Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.

Linear Algebra and Geometry

Author: Kam-Tim Leung

Publisher: Hong Kong University Press

ISBN: 0856561118

Category: Mathematics

Page: 320

View: 902

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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.

Matrices and Linear Transformations

Second Edition

Author: Charles G. Cullen

Publisher: Courier Corporation

ISBN: 0486132412

Category: Mathematics

Page: 336

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Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.

Introduction to Matrices and Vectors

Author: Jacob T. Schwartz

Publisher: Courier Corporation

ISBN: 0486143708

Category: Mathematics

Page: 192

View: 5512

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DIVIn this concise undergraduate text, the first three chapters present the basics of matrices — in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition. /div

A First Course in Linear Algebra

Author: Daniel Zelinsky

Publisher: Academic Press

ISBN: 1483265005

Category: Mathematics

Page: 276

View: 1918

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A First Course in Linear Algebra provides an introduction to the algebra and geometry of vectors, matrices, and linear transformations. This book is designed as a background for second-year courses in calculus of several variables and differential equations where the theory of linear differential equations parallels that of linear algebraic equations. The topics discussed include the multiplication of vectors by scalars, vectors in n-space, planes and lines, and composites of linear mappings. The symmetric matrices and mappings, quadratic forms, change of coordinates, and effect of change of basis on matrices of linear functions are also described. This text likewise considers the computation of determinants, diagonalizable transformations, computation of eigenvalues and eigenvectors, and principal axis theorem. This publication is suitable for college students taking a course in linear algebra.

Linear Algebra and Geometry

Author: Igor R. Shafarevich,Alexey O. Remizov

Publisher: Springer Science & Business Media

ISBN: 3642309941

Category: Mathematics

Page: 526

View: 4207

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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.

Groups, Matrices, and Vector Spaces

A Group Theoretic Approach to Linear Algebra

Author: James B. Carrell

Publisher: Springer

ISBN: 038779428X

Category: Mathematics

Page: 410

View: 1894

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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.

A Vector Space Approach to Geometry

Author: Melvin Hausner

Publisher: Courier Dover Publications

ISBN: 0486835391

Category: Mathematics

Page: 416

View: 6101

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A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.

Linear Algebra and Analytic Geometry for Physical Sciences

Author: Giovanni Landi,Alessandro Zampini

Publisher: Springer

ISBN: 3319783610

Category: Science

Page: 345

View: 3807

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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.

Linear Algebra Through Geometry

Author: Thomas Banchoff,John Wermer

Publisher: Springer Science & Business Media

ISBN: 1461243904

Category: Mathematics

Page: 308

View: 5603

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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.

Linear Algebra: A Modern Introduction

Author: David Poole

Publisher: Cengage Learning

ISBN: 0538735457

Category: Mathematics

Page: 768

View: 4492

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David Poole’s innovative book emphasizes vectors and geometric intuition from the start and better prepares students to make the transition from the computational aspects of the course to the theoretical. Designed for a one- or two-semester introductory course and written in simple, mathematical English Poole focuses his approach on benefiting student visualization and connection to the material. He offers concrete examples to engage the student before presenting abstraction, and immediately follows up theoretical discussion with further examples and an array of applications from a variety of disciplines. Students from a variety of backgrounds and learning styles benefit from Poole’s practical approach, which covers vectors and vector geometry early in order to enable students to visualize the mathematics while they are doing matrix operations. With a concrete understanding of vector geometry, students are able to visualize and understand the meaning of the calculations that they will encounter and develop mathematical maturity for thinking abstractly. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Vector Geometry

Author: Gilbert de B. Robinson

Publisher: Courier Corporation

ISBN: 0486321045

Category: Mathematics

Page: 192

View: 1156

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Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.

Geometric Linear Algebra

Author: I-Hsiung Lin

Publisher: World Scientific

ISBN: 9812707751

Category: Mathematics

Page: 806

View: 8949

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This accessible book for beginners uses intuitive geometric concepts to create abstract algebraic theory with a special emphasis on geometric characterizations. The book applies known results to describe various geometries and their invariants, and presents problems concerned with linear algebra, such as in real and complex analysis, differential equations, differentiable manifolds, differential geometry, Markov chains and transformation groups. The clear and inductive approach makes this book unique among existing books on linear algebra both in presentation and in content.

Linear algebra and geometry

Author: Nicolaas Hendrik Kuiper

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 284

View: 2913

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Vectors in the plane and in space; Subset, product set, relation and mapping; The n-dimensional vector space V; The parametric representation of a line; Some fundamental theorems; The dual vector space V*; Firts degree function on, and linear varieties in A; Linear function and lines in A2 and A. application cross-ratio; Harmonic separation; A finite affine plane; Homomorphisms of vector spaces; The vector space hom (A, B); Composition (multiplication) of homomorphisms; The dual homomorphism of the dual vector spaces; Matrices.

Vectors, Matrices and C++ Code

Author: Sergio Pissanetzky

Publisher: N.A

ISBN: 0976277506

Category: Computers

Page: 365

View: 5506

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Presented here is an integrated approach - perhaps the first in its class - of the basics of vector and matrix Algebra at College level, with the object-oriented C++ code that implements the vector and matrix objects and brings them to life. Thinking in terms of objects is the natural way of thinking. The concept of object has existed in Science for centuries. More recently, objects were introduced in Computation, and object-oriented programming languages were created. Yet the concept of object is not routinely used when teaching Science, and the idea that objects can come alive in a computer has not yet been fully exploited.This book integrates basic vector and matrix Algebra with object-oriented concepts and the actual code implementing them. It is both a textbook and a software release, complete withsoftware documentation and the mathematical background that supports the code. The source code is included by download and readers can use it for their own programming. The reader will need a basic knowledge of Mathematical notation, Algebra and Trigonometry, but familiarity with C++ is not required because a course on C++ is also included. You should read this book if you are a developer who needs a background in vector or matrix algebra, a science student who needs tolearn C++, a scientist who needs to write advanced code but can't waste time developing the basics, or you just need ready-to-use C++ source code for your project.

Linear algebra

Author: John B. Fraleigh,Raymond A. Beauregard

Publisher: Addison Wesley Publishing Company

ISBN: N.A

Category: Mathematics

Page: 477

View: 6857

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Fraleigh and Beauregard's text is known for its clear presentation and writing style, mathematical appropriateness, and overall usability. Its inclusion of calculus-related examples, true/false problems, section summaries, integrated applications, and coverage of Cn make it a superb text for the sophomore or junior-level linear algebra course. This Third Edition retains the features that have made it successful over the years, while addressing recent developments of how linear algebra is taught and learned. Key concepts are presented early on, with an emphasis on geometry. KEY TOPICS: Vectors, Matrices, and Linear Systems; Dimension, Rank, and Linear Transformations; Vector Spaces; Determinants; Eigenvalues and Eigenvectors; Orthogonality; Change of Basis; Eigenvalues: Further Applications and Computations; Complex Scalars; Solving Large Linear Systems MARKET: For all readers interested in linear algebra.