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Author: Melvin Hausner
Publisher: Courier Dover Publications
ISBN: 0486835391
Category : Mathematics
Languages : en
Pages : 417
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Book Description
A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
Author: Melvin Hausner
Publisher: Courier Dover Publications
ISBN: 0486835391
Category : Mathematics
Languages : en
Pages : 417
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Book Description
A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
Author: Igor R. Shafarevich
Publisher: Springer Science & Business Media
ISBN: 3642309941
Category : Mathematics
Languages : en
Pages : 536
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Book Description
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: Gilbert de B. Robinson
Publisher: Courier Corporation
ISBN: 0486321045
Category : Mathematics
Languages : en
Pages : 194
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Book Description
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.
Author: Max Jeger
Publisher: Interscience Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Translation of Einfèuhrung in die vektorielle Geometrie und lineare Algebra (fèur Ingenieure und Naturwissenschafter)
Author: K.T. Leung
Publisher: Hong Kong University Press
ISBN: 9622093604
Category : Mathematics
Languages : en
Pages : 357
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Book Description
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).
Author: Thomas Banchoff
Publisher: Springer Science & Business Media
ISBN: 1461243904
Category : Mathematics
Languages : en
Pages : 316
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Book Description
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: Bruce Solomon
Publisher: CRC Press
ISBN: 1482299305
Category : Mathematics
Languages : en
Pages : 474
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Book Description
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: Stephen Boyd
Publisher: Cambridge University Press
ISBN: 1316518965
Category : Business & Economics
Languages : en
Pages : 477
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Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author:
Publisher: Krishna Prakashan Media
ISBN:
Category :
Languages : en
Pages : 572
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Book Description
Author: E. Sernesi
Publisher: Routledge
ISBN: 1351435280
Category : Mathematics
Languages : en
Pages : 274
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Book Description
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
