Linear Algebra And Projective Geometry PDF Download
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| Author | : Reinhold Baer |
| Publisher | : Courier Corporation |
| Total Pages | : 338 |
| Release | : 2012-06-11 |
| Genre | : Mathematics |
| ISBN | : 0486154661 |
Download Linear Algebra and Projective Geometry Book in PDF, ePub and Kindle
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.
| Author | : Igor R. Shafarevich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 536 |
| Release | : 2012-08-23 |
| Genre | : Mathematics |
| ISBN | : 3642309941 |
Download Linear Algebra and Geometry Book in PDF, ePub and Kindle
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 | : |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1979 |
| Genre | : |
| ISBN | : |
Download Algebraic Projective Geometry Book in PDF, ePub and Kindle
| Author | : Lars Kadison |
| Publisher | : Birkhäuser Boston |
| Total Pages | : 228 |
| Release | : 1996-01-26 |
| Genre | : Mathematics |
| ISBN | : 0817639004 |
Download Projective Geometry and Modern Algebra Book in PDF, ePub and Kindle
The techniques and concepts of modern algebra are introduced for their natural role in the study of projectile geometry; groups appear as automorphism groups of configurations, division rings appear in the study of Desargues' theorem and the study of the independence of the seven axioms given for projectile geometry.
| Author | : C. R. Wylie |
| Publisher | : Courier Corporation |
| Total Pages | : 578 |
| Release | : 2011-09-12 |
| Genre | : Mathematics |
| ISBN | : 0486141705 |
Download Introduction to Projective Geometry Book in PDF, ePub and Kindle
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
| Author | : K. W. Gruenberg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 208 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1475741014 |
Download Linear Geometry Book in PDF, ePub and Kindle
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.
| Author | : M. K. Bennett |
| Publisher | : John Wiley & Sons |
| Total Pages | : 251 |
| Release | : 2011-02-14 |
| Genre | : Mathematics |
| ISBN | : 1118030826 |
Download Affine and Projective Geometry Book in PDF, ePub and Kindle
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.
| Author | : P. K. Suetin |
| Publisher | : CRC Press |
| Total Pages | : 324 |
| Release | : 1997-10-01 |
| Genre | : Mathematics |
| ISBN | : 9789056990497 |
Download Linear Algebra and Geometry Book in PDF, ePub and Kindle
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.
| Author | : Albrecht Beutelspacher |
| Publisher | : Cambridge University Press |
| Total Pages | : 272 |
| Release | : 1998-01-29 |
| Genre | : Mathematics |
| ISBN | : 9780521483643 |
Download Projective Geometry Book in PDF, ePub and Kindle
Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.
| Author | : Jürgen Richter-Gebert |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 573 |
| Release | : 2011-02-04 |
| Genre | : Mathematics |
| ISBN | : 3642172865 |
Download Perspectives on Projective Geometry Book in PDF, ePub and Kindle
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
