Affine And Metric Geometry Based On Linear Algebra
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Metric Affine Geometry
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Author : Ernst Snapper
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Metric Affine Geometry written by Ernst Snapper and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers.
Linear Algebra
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Author : E. Sernesi
language : en
Publisher: Routledge
Release Date : 2019-01-22
Linear Algebra written by E. Sernesi and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-22 with Mathematics categories.
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
Linear Algebra And Geometry
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Author : P. K. Suetin
language : en
Publisher: CRC Press
Release Date : 1989-07-14
Linear Algebra And Geometry written by P. K. Suetin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07-14 with Mathematics categories.
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
Analytic Projective Geometry
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Author : Eduardo Casas-Alvero
language : en
Publisher: Susaeta
Release Date : 2014
Analytic Projective Geometry written by Eduardo Casas-Alvero and has been published by Susaeta this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Geometry, Analytic categories.
Projective geometry is concerned with the properties of figures that are invariant by projecting and taking sections. It is considered one of the most beautiful parts of geometry and plays a central role because its specializations cover the whole of the affine, Euclidean and non-Euclidean geometries. The natural extension of projective geometry is projective algebraic geometry, a rich and active field of research. The results and techniques of projective geometry are intensively used in computer vision. This book contains a comprehensive presentation of projective geometry, over the real and complex number fields, and its applications to affine and Euclidean geometries. It covers central topics such as linear varieties, cross ratio, duality, projective transformations, quadrics and their classifications--projective, affine and metric--as well as the more advanced and less usual spaces of quadrics, rational normal curves, line complexes and the classifications of collineations, pencils of quadrics and correlations. Two appendices are devoted to the projective foundations of perspective and to the projective models of plane non-Euclidean geometries. The book uses modern language, is based on linear algebra, and provides complete proofs. Exercises are proposed at the end of each chapter; many of them are beautiful classical results. The material in this book is suitable for courses on projective geometry for undergraduate students, with a working knowledge of a standard first course on linear algebra. The text is a valuable guide to graduate students and researchers working in areas using or related to projective geometry, such as algebraic geometry and computer vision, and to anyone looking for an advanced view of geometry as a whole.
Linear Geometry
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Author : K. W. Gruenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Linear Geometry written by K. W. Gruenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
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.
Linear Algebra And Geometry
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Author : Nicolaas Hendrik Kuiper
language : en
Publisher:
Release Date : 1965
Linear Algebra And Geometry written by Nicolaas Hendrik Kuiper and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Mathematics categories.
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.
Affine And Metric Geometry Based On Linear Algebra
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Author : Ernst Snapper
language : en
Publisher:
Release Date : 1967
Affine And Metric Geometry Based On Linear Algebra written by Ernst Snapper and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Geometry, Affine categories.
Linear Algebra And Geometry
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Author : P. K. Suetin
language : en
Publisher: CRC Press
Release Date : 1997-10-01
Linear Algebra And Geometry written by P. K. Suetin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-01 with Mathematics categories.
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.
Linear Algebra And Geometry
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Author : James A. Murtha
language : en
Publisher:
Release Date : 1969
Linear Algebra And Geometry written by James A. Murtha and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
Linear Algebra And Projective Geometry
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Author : Reinhold Baer
language : en
Publisher: Courier Corporation
Release Date : 2012-06-11
Linear Algebra And Projective Geometry written by Reinhold Baer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-11 with Mathematics categories.
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.