Vectors, Matrices and Geometry

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

Publisher: Hong Kong University Press

ISBN: 9622093604

Category: Mathematics

Page: 356

View: 5421


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).

Matrices and Linear Transformations

Second Edition

Author: Charles G. Cullen

Publisher: Courier Corporation

ISBN: 0486132412

Category: Mathematics

Page: 336

View: 4776


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: 2757


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 Vector Space Approach to Geometry

Author: Melvin Hausner

Publisher: Courier Dover Publications

ISBN: 0486835391

Category: Mathematics

Page: 416

View: 2782


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.

Vector Geometry

Author: Gilbert de B. Robinson

Publisher: Courier Corporation

ISBN: 0486321045

Category: Mathematics

Page: 192

View: 785


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.

Linear Algebra and Geometry

Author: Igor R. Shafarevich,Alexey Remizov

Publisher: Springer Science & Business Media

ISBN: 3642309941

Category: Mathematics

Page: 526

View: 6072


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: 1840


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.

Linear Algebra Through Geometry

Author: Thomas Banchoff,John Wermer

Publisher: Springer Science & Business Media

ISBN: 1461243904

Category: Mathematics

Page: 308

View: 6215


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 and Analytic Geometry for Physical Sciences

Author: Giovanni Landi,Alessandro Zampini

Publisher: Springer

ISBN: 3319783610

Category: Science

Page: 345

View: 1705


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.

Matrix Vector Analysis

Author: Richard L. Eisenman

Publisher: Courier Corporation

ISBN: 0486154572

Category: Mathematics

Page: 320

View: 4861


This outstanding text and reference for upper-level undergraduates features extensive problems and solutions in its application of matrix ideas to vector methods for a synthesis of pure and applied mathematics. 1963 edition. Includes 121 figures.

Matrices and Linear Algebra

Author: Hans Schneider,George Phillip Barker

Publisher: Courier Corporation

ISBN: 0486139301

Category: Mathematics

Page: 432

View: 2846


Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues, and differential equations. Includes numerous exercises.

Geometry of Matrices

Author: Zhexian Wan,Luogeng Hua

Publisher: World Scientific

ISBN: 9789810226381

Category: Mathematics

Page: 376

View: 4900


The present monograph is a state-of-art survey of the geometry of matrices whose study was initiated by L K Hua in the forties. The geometry of rectangular matrices, of alternate matrices, of symmetric matrices, and of hermitian matrices over a division ring or a field are studied in detail. The author's recent results on geometry of symmetric matrices and of hermitian matrices are included. A chapter on linear algebra over a division ring and one on affine and projective geometry over a division ring are also included. The book is clearly written so that graduate students and third or fourth year undergraduate students in mathematics can read it without difficulty.

Introduction to Matrices and Linear Transformations

Author: Daniel T. Finkbeiner

Publisher: Courier Corporation

ISBN: 048648159X

Category: Mathematics

Page: 462

View: 1832


This versatile undergraduate text can be used in a variety of courses in linear algebra. It contains enough material for a one-year course, and it also serves as a support text and reference. A combination of formal theory and related computational techniques, it includes solutions to selected exercises. 1978 edition.

Linear algebra

Author: John B. Fraleigh,Raymond A. Beauregard

Publisher: Addison Wesley Publishing Company


Category: Mathematics

Page: 477

View: 9395


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.

Linear Algebra: A Modern Introduction

Author: David Poole

Publisher: Cengage Learning

ISBN: 1285463242

Category: Mathematics

Page: 720

View: 8418


David Poole's innovative LINEAR ALGEBRA: A MODERN INTRODUCTION, 4e emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Matrices and Transformations

Author: Anthony J. Pettofrezzo

Publisher: Courier Corporation

ISBN: 9780486636344

Category: Mathematics

Page: 133

View: 8461


This book presents an elementary and concrete approach to linear algebra that is both useful and essential for the beginning student and teacher of mathematics. Here are the fundamental concepts of matrix algebra, first in an intuitive framework and then in a more formal manner. A Variety of interpretations and applications of the elements and operations considered are included. In particular, the use of matrices in the study of transformations of the plane is stressed. The purpose of this book is to familiarize the reader with the role of matrices in abstract algebraic systems, and to illustrate its effective use as a mathematical tool in geometry. The first two chapters cover the basic concepts of matrix algebra that are important in the study of physics, statistics, economics, engineering, and mathematics. Matrices are considered as elements of an algebra. The concept of a linear transformation of the plane and the use of matrices in discussing such transformations are illustrated in Chapter #. Some aspects of the algebra of transformations and its relation to the algebra of matrices are included here. The last chapter on eigenvalues and eigenvectors contains material usually not found in an introductory treatment of matrix algebra, including an application of the properties of eigenvalues and eigenvectors to the study of the conics. Considerable attention has been paid throughout to the formulation of precise definitions and statements of theorems. The proofs of most of the theorems are included in detail in this book. Matrices and Transformations assumes only that the reader has some understanding of the basic fundamentals of vector algebra. Pettofrezzo gives numerous illustrative examples, practical applications, and intuitive analogies. There are many instructive exercises with answers to the odd-numbered questions at the back. The exercises range from routine computations to proofs of theorems that extend the theory of the subject. Originally written for a series concerned with the mathematical training of teachers, and tested with hundreds of college students, this book can be used as a class or supplementary text for enrichments programs at the high school level, a one-semester college course, individual study, or for in-service programs.

Vectors, Matrices and C++ Code

Author: Sergio Pissanetzky

Publisher: N.A

ISBN: 0976277506

Category: Computers

Page: 365

View: 3849


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.

A First Course in Linear Algebra

Author: Daniel Zelinsky

Publisher: Academic Press

ISBN: 1483265005

Category: Mathematics

Page: 276

View: 559


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.