Vectors Matrices And Geometry

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Vectors, Matrices and Geometry

Author : K.T. Leung
Publisher : Hong Kong University Press
ISBN 13 : 9622093604
Total Pages : 357 pages
Book Rating : 4.6/5 (22 download)

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Book Synopsis Vectors, Matrices and Geometry by : K.T. Leung

Download or read book Vectors, Matrices and Geometry written by K.T. Leung and published by Hong Kong University Press. This book was released on 1994-08-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Vector Geometry

Author : Gilbert de B. Robinson
Publisher : Courier Corporation
ISBN 13 : 0486321045
Total Pages : 194 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Vector Geometry by : Gilbert de B. Robinson

Download or read book Vector Geometry written by Gilbert de B. Robinson and published by Courier Corporation. This book was released on 2013-10-10 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analytic Geometry with an Introduction to Vectors and Matrices

Author : David Carruthers Murdoch
Publisher : New York : J. Wiley & Sons
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Analytic Geometry with an Introduction to Vectors and Matrices by : David Carruthers Murdoch

Download or read book Analytic Geometry with an Introduction to Vectors and Matrices written by David Carruthers Murdoch and published by New York : J. Wiley & Sons. This book was released on 1966 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Vector Space Approach to Geometry

Author : Melvin Hausner
Publisher : Courier Dover Publications
ISBN 13 : 0486835391
Total Pages : 417 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis A Vector Space Approach to Geometry by : Melvin Hausner

Download or read book A Vector Space Approach to Geometry written by Melvin Hausner and published by Courier Dover Publications. This book was released on 2018-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Matrices and Vectors

Author : Jacob T. Schwartz
Publisher : Courier Corporation
ISBN 13 : 0486143708
Total Pages : 198 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to Matrices and Vectors by : Jacob T. Schwartz

Download or read book Introduction to Matrices and Vectors written by Jacob T. Schwartz and published by Courier Corporation. This book was released on 2012-05-23 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Multiplication of Vectors

Author : Miroslav Josipović
Publisher : Springer Nature
ISBN 13 : 3030017567
Total Pages : 241 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Geometric Multiplication of Vectors by : Miroslav Josipović

Download or read book Geometric Multiplication of Vectors written by Miroslav Josipović and published by Springer Nature. This book was released on 2019-11-22 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it, and undergraduate students can master it. The universality, the clear geometric interpretation, the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth.

Vectors and Matrices for Geometric and 3D Modeling

Author : Michael Mortenson
Publisher : Industrial Press
ISBN 13 : 9780831136550
Total Pages : 350 pages
Book Rating : 4.1/5 (365 download)

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Book Synopsis Vectors and Matrices for Geometric and 3D Modeling by : Michael Mortenson

Download or read book Vectors and Matrices for Geometric and 3D Modeling written by Michael Mortenson and published by Industrial Press. This book was released on 2020-04-15 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Linear Algebra Through Geometry

Author : Thomas Banchoff
Publisher : Springer Science & Business Media
ISBN 13 : 1461243904
Total Pages : 316 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Linear Algebra Through Geometry by : Thomas Banchoff

Download or read book Linear Algebra Through Geometry written by Thomas Banchoff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Springer
ISBN 13 : 3319783610
Total Pages : 348 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Linear Algebra and Analytic Geometry for Physical Sciences by : Giovanni Landi

Download or read book Linear Algebra and Analytic Geometry for Physical Sciences written by Giovanni Landi and published by Springer. This book was released on 2018-05-12 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Vector Geometry and Linear Algebra

Author : Max Jeger
Publisher : Interscience Publishers
ISBN 13 :
Total Pages : 276 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Vector Geometry and Linear Algebra by : Max Jeger

Download or read book Vector Geometry and Linear Algebra written by Max Jeger and published by Interscience Publishers. This book was released on 1967 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translation of Einfèuhrung in die vektorielle Geometrie und lineare Algebra (fèur Ingenieure und Naturwissenschafter)

Groups, Matrices, and Vector Spaces

Author : James B. Carrell
Publisher : Springer
ISBN 13 : 038779428X
Total Pages : 415 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Groups, Matrices, and Vector Spaces by : James B. Carrell

Download or read book Groups, Matrices, and Vector Spaces written by James B. Carrell and published by Springer. This book was released on 2017-09-02 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elementary Vector Geometry

Author : Seymour Schuster
Publisher :
ISBN 13 :
Total Pages : 228 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Elementary Vector Geometry by : Seymour Schuster

Download or read book Elementary Vector Geometry written by Seymour Schuster and published by . This book was released on 2008 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Appropriate for high school and college courses, this elementary text addresses the development of vector algebra as a mathematical tool and features applications to trigonometry and algebra. Exercises, solutions. 1962 edition.

Introduction to Applied Linear Algebra

Author : Stephen Boyd
Publisher : Cambridge University Press
ISBN 13 : 1316518965
Total Pages : 477 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd

Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Vectors and Matrices

Author : Pamela Liebeck
Publisher : Elsevier
ISBN 13 : 1483280438
Total Pages : 193 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Vectors and Matrices by : Pamela Liebeck

Download or read book Vectors and Matrices written by Pamela Liebeck and published by Elsevier. This book was released on 2014-05-09 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Vector Geometry

Author : Gilbert de Beauregard Robinson
Publisher : Independently Published
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.5/5 (866 download)

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Book Synopsis Vector Geometry by : Gilbert de Beauregard Robinson

Download or read book Vector Geometry written by Gilbert de Beauregard Robinson and published by Independently Published. This book was released on 2020-12-25 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This then was the problem-to give an introductory course in modern algebra and geometry-and I have proceeded on the assumption that neither is complete without the other, that they are truly two sides of the same coin. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geometry, geometry on the sphere, and reduction of real matrices to diagonal form. Exercises appear throughout the text, with complete answers at the end. In seeking to coordinate Euclidean, projective, and non-Euclidean geometry in an elementary way with matrices, determinants, and linear transformations, the notion of a vector has been exploited to the full. There is nothing new in this book, but an attempt has been made to present ideas at a level suitable to first-year students and in a manner to arouse their interest. For these associations of ideas are the stuff from which modern mathematics and many of its applications are made. I have tried to keep the presentation as informal as possible in an attempt to arouse and maintain interest. Some of your established ideas may be challenged in Chapter 8 but this is all part of the process! The exercises have been constructed to illustrate the subject in hand and sometimes to carry the ideas a little further, but emphasis by mere repetition has been avoided. This matter of exercises is important. You should work at them contemplatively and expect to be frustrated sometimes, for this is the only way to make the ideas your own. The notion of a vector is of central significance in Euclidean geometry. As the title of this book suggests, our purpose is to develop these ideas in several different contexts. Some of these contexts are officially "algebraic" while others are "geometric," but with this thread to guide us, we shall see their interrelations and why it is that mathematics is a living subject, changing and progressing with the introduction of new ideas.

Clifford Algebra to Geometric Calculus

Author : David Hestenes
Publisher : Springer Science & Business Media
ISBN 13 : 9789027725615
Total Pages : 340 pages
Book Rating : 4.7/5 (256 download)

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Book Synopsis Clifford Algebra to Geometric Calculus by : David Hestenes

Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes and published by Springer Science & Business Media. This book was released on 1984 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.

Linear Algebra and Geometry

Author : Nicolaas Hendrik Kuiper
Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Linear Algebra and Geometry by : Nicolaas Hendrik Kuiper

Download or read book Linear Algebra and Geometry written by Nicolaas Hendrik Kuiper and published by . This book was released on 1965 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.