Download or read book Metric Affine Geometry written by Ernst Snapper and published by Elsevier. This book was released on 2014-05-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Affine and Metric Geometry Based on Linear Algebra written by Ernst Snapper and published by . This book was released on 1967 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Algebra written by E. Sernesi and published by Routledge. This book was released on 2019-01-22 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Linear Algebra and Geometry written by Francesco Bottacin and published by Società Editrice Esculapio. This book was released on 2023-05-25 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originates from the lessons held by the author in university courses and is aimed at students who, for the first time, are approaching a course in linear algebra and geometry. Bearing in mind the difficulties that students usually encounter in the study of abstract topics such as those presented in this book, we have chosen to use a language that is as simple as possible, trying to motivate the introduction of the various abstract notions with concrete examples. Topics covered include the theory of vector spaces and linear functions, the theory of matrices and systems of linear equations, the theory of Euclidean vector spaces and, finally, the applications of linear algebra to the study of the geometry of affine space. Numerous figures, examples and exercises carried out in every detail have been included in order to facilitate the study and understanding of the topics presented.
Download or read book Affine Maps Euclidean Motions and Quadrics written by Agustí Reventós Tarrida and published by Springer Science & Business Media. This book was released on 2011-06-01 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Affine geometry and quadrics are fascinating subjects alone, but they are also important applications of linear algebra. They give a first glimpse into the world of algebraic geometry yet they are equally relevant to a wide range of disciplines such as engineering. This text discusses and classifies affinities and Euclidean motions culminating in classification results for quadrics. A high level of detail and generality is a key feature unmatched by other books available. Such intricacy makes this a particularly accessible teaching resource as it requires no extra time in deconstructing the author’s reasoning. The provision of a large number of exercises with hints will help students to develop their problem solving skills and will also be a useful resource for lecturers when setting work for independent study. Affinities, Euclidean Motions and Quadrics takes rudimentary, and often taken-for-granted, knowledge and presents it in a new, comprehensive form. Standard and non-standard examples are demonstrated throughout and an appendix provides the reader with a summary of advanced linear algebra facts for quick reference to the text. All factors combined, this is a self-contained book ideal for self-study that is not only foundational but unique in its approach.’ This text will be of use to lecturers in linear algebra and its applications to geometry as well as advanced undergraduate and beginning graduate students.
Download or read book Linear Algebra and Geometry written by P. K. Suetin and published by CRC Press. This book was released on 1997-10-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Algebra and Geometry written by P. K. Suetin and published by CRC Press. This book was released on 1989-07-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Linear Algebra and Geometry written by Kam-Tim Leung and published by Hong Kong University Press. This book was released on 1974-01-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Affine and Projective Geometry written by M. K. Bennett and published by John Wiley & Sons. This book was released on 2011-02-14 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important new perspective on AFFINE AND PROJECTIVEGEOMETRY This innovative book treats math majors and math education studentsto a fresh look at affine and projective geometry from algebraic,synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninetyillustrations, and numerous examples and exercises, coveringmaterial for two semesters of upper-level undergraduatemathematics. The first part of the book deals with the correlationbetween synthetic geometry and linear algebra. In the second part,geometry is used to introduce lattice theory, and the bookculminates with the fundamental theorem of projectivegeometry. While emphasizing affine geometry and its basis in Euclideanconcepts, the book: * Builds an appreciation of the geometric nature of linear algebra * Expands students' understanding of abstract algebra with itsnontraditional, geometry-driven approach * Demonstrates how one branch of mathematics can be used to provetheorems in another * Provides opportunities for further investigation of mathematicsby various means, including historical references at the ends ofchapters Throughout, the text explores geometry's correlation to algebra inways that are meant to foster inquiry and develop mathematicalinsights whether or not one has a background in algebra. Theinsight offered is particularly important for prospective secondaryteachers who must major in the subject they teach to fulfill thelicensing requirements of many states. Affine and ProjectiveGeometry's broad scope and its communicative tone make it an idealchoice for all students and professionals who would like to furthertheir understanding of things mathematical.
Download or read book Linear Algebra and Geometry written by Igor R. Shafarevich and published by Springer Science & Business Media. This book was released on 2012-08-23 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Geometry written by K. W. Gruenberg and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Affine and Euclidean Geometry written by Robert J. Troyer and published by . This book was released on 1967 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exercises in Linear Algebra and Geometry written by Francesco Bottacin and published by Società Editrice Esculapio. This book was released on 2023-09-27 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of exercises designed to support and complement the theoretical exposition of the standard topics for a first course in linear algebra and geometry, at university level. In this sense, this exercise book is a natural completion of the text F. Bottacin, Linear Algebra and Geometry, Esculapio, Bologna which will be referred to for the necessary theoretical notions. In presenting the solutions to the proposed exercises, my main goal is to try to teach how to approach and solve a problem. For this reason, in many cases, theoretical considerations have been included and different solution methods have been proposed for the same type of exercise. The reader will thus be able to evaluate, case by case, the advantages and disadvantages of each method.
Download or read book Analytic Projective Geometry written by Eduardo Casas-Alvero and published by Susaeta. This book was released on 2014 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Algebra and Projective Geometry written by Reinhold Baer and published by Courier Corporation. This book was released on 2012-06-11 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Affinite and Metric Geometry Based on Linear Algebra written by Ernst Snapper and published by . This book was released on 1967 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Algebra and Geometry written by James A. Murtha and published by . This book was released on 1969 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
