Linear algebra and projective geometry.

Cover of: Linear algebra and projective geometry. | Reinhold Baer

Published by Academic Press in New York .

Written in English

Read online

Subjects:

  • Geometry, Projective.,
  • Transformations (Mathematics)

Edition Notes

Includes bibliography.

Book details

SeriesPure and applied mathematics (Academic Press) ;, 2
Classifications
LC ClassificationsQA3 .P8 vol. 2
The Physical Object
Pagination318 p.
Number of Pages318
ID Numbers
Open LibraryOL6111054M
LC Control Number52007480
OCLC/WorldCa339910

Download Linear algebra and projective geometry.

out of 5 stars Linear Algebra and projective geometry Dover. Reviewed in the United States on May 2, Format: Paperback Verified Purchase. The book makes a systematic approach to show that linear algebra and projective geometry are Cited by: out of 5 stars Linear Algebra and projective geometry Dover.

Reviewed in the United States on May 2, Format: Paperback Verified Purchase. The book makes a systematic approach to show that linear algebra and projective geometry are mathematically equivalent/5(4). Get this from a library.

Linear algebra and projective geometry. [Reinhold Baer] -- This book establishes the essential structural identity of projective geometry and linear algebra. The fundamental existence theorems, wherein geometrical.

vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. Another standard is book’s audience: sophomores or juniors, usually with a. Analytic projective geometry uses linear algebra. For instance, for three points of the projective plane t, u, v {\displaystyle t,u,v}, setting up the equations for those points by fixing vectors representing each, shows that the three are collinear — incident in a single line — if and only if the resulting three-equation system has.

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.

These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point. 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. These theorems lead to a Author: Reinhold Baer.

Purchase Linear algebra and projective geometry, Volume 2 - 1st Edition. Print Book & E-Book. ISBNBook Edition: 1. Linear algebra and projective geometry. book Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students.

Linear algebra and projective geometry. book Audin, professor at the University of Strasbourg, has written a book allowing them to remedy this situation and, starting from linear algebra, extend their knowledge of affine, Euclidean and projective geometry, conic sections and quadrics, curves and surfaces.

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.

These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear. Problem 5. Give a drawing to show that central projection does not preserve circles, that a circle may project to an ellipse.

Can a (non-circular) ellipse project to a circle. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point. Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical.3/5.

The fourth chapter of the book is the most difficult and probably one that is not easily accessible to most undergraduates.

In this chapter, the author begins by departing from the linear-algebraic approach to geometry and instead looks at the axiomatic foundations of affine and projective (plane) geometry. 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.

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. edition. Category: Mathematics Affine And Projective Geometry. In span of pages, there are only 19 diagrams and, although the ideas from linear algebra are invoked throughout the book, matrices are hardly used at all.

The main thrust is a series of theorems on the representation of projective geometries by linear manifolds and of collineations by linear transformations and of dualities by semilinear forms.

Linear Algebra and Projective Geometry by Reinhold Baer,available at Book Depository with free delivery worldwide.3/5(2). In mathematics, especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear group of a vector space V on the associated projective space P(V).Explicitly, the projective linear group is the quotient group.

PGL(V) = GL(V)/Z(V)where GL(V) is the general linear group of V. The material is standard in that the subjects covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors.

Another standard is book’s audience: sophomores or juniors, usually with a background of at least one semester of calculus. Master MOSIG Introduction to Projective Geometry A B C A B C R R R Figure The projective space associated to R3 is called the projective plane P2.

De nition (Algebraic De nition) A point of a real projective space Pn is represented by a vector of real coordinates X = [xFile Size: KB. Projective geometry is a topic in is the study of geometric properties that are invariant with respect to projective means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric basic intuitions are that projective space has more points than.

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. Get this from a library.

Linear algebra and projective geometry. [Reinhold Baer] -- 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. Coxeter's "Projective Geometry" is a really good small book and a quick read, but since it is a purely synthetic approach, it will probably only be useful to you if you are interested in origins. permalink.

In this post, we will see the book Linear Algebra And Multi Dimensional Geometry by N. Efimov, E. Rozendorn About the book This book was conceived as a text combining the course of linear algebra and analytic geometry.

It originated as a course of lectures delivered by N. Efimov at Moscow State University. Differential, Projective, and Synthetic Geometry General Investigations of Curved Surfaces of andby Carl Friedrich Gauss An Elementary Course in Synthetic Projective Geometry by Lehmer Author: Kevin de Asis.

aic subsets of Pn, ; Zariski topology on Pn, ; subsets of A nand P, ; hyperplane at infinity, ; an algebraic variety, ; f. The homogeneous coordinate ring of a projective variety, ; r functions on a projective variety, ; from projective varieties, ; classical maps of.

Introduction to Algebraic Geometry by Igor V. Dolgachev. This book explains the following topics: Systems of algebraic equations, Affine algebraic sets, Morphisms of affine algebraic varieties, Irreducible algebraic sets and rational functions, Projective algebraic varieties, Morphisms of projective algebraic varieties, Quasi-projective algebraic sets, The image of a projective.

A very good introduction to the geometry of linear algebra is Linear Algebra and Geometry: A Second Course by Irving Kaplansky. This is a strongly rigorous and abstract treatment by one of the masters of algebra of the last century.

it focuses largely on the geometry of inner product and projective spaces,which are very naturally expressed in. In seeking to coordinate Euclidean, projective, and non-Euclidean geometry in an elementary way with matrices, determinants, and linear transformations, the.

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. Linear Algebra and Projective Geometry | Reinhold Baer | download | B–OK. Download books for free. Find books.

Linear Algebra and Projective Geometry. by Reinhold Baer. Dover Books on Mathematics. Share your thoughts Complete your review. Tell readers what you thought by rating and reviewing this book. Rate it * You Rated it *Brand: Dover Publications. 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.

A classic in linear algebra is Paul R. Halmos' Linear Algebra Problem Book. In fact it's also a great book teaching many aspects of linear algebra and a great book in teaching how to solve first part contains more than problems, the last part contains detailed solutions.

Linear algebra itself will be a subject of high relevance for the far foreseeable future, and this book does a good job of capturing the major important points of what is now consider the classical core of linear algebra, and even extends a bit beyond this/5(7).

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 5/5(1). This is a good contemporary book on linear algebra. It would be appropriate for any sophomore-level linear algebra course for pure math, applied math, CS, or related fields.

It includes some nice sections on computing that could lead naturally into a course on numerical methods. Clarity rating: 5 The text is very clear/5(4). This book was conceived as a text combining the course of linear algebra and analytic geometry. It originated as a course of lectures delivered by N.

Efimov at Moscow State University (mechanics and mathematics department) in However, the material of these lectures has been completely reworked and substantially expanded. Summary. 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. Hardback or Cased Book. Condition: New.

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By P. K. Suetin, Alexandra I. Kostrikin, Yu I Manin. Edition 1st Edition. First Published eBook Published 14 July Pub. location London. Imprint CRC Press. Affine and Projective : P. K. Suetin, Alexandra I. Kostrikin, Yu I Manin.The first part of the book deals with the correlation between synthetic geometry and linear algebra.

In the second part, geometry is used to introduce lattice theory, and the book culminates with the fundamental theorem of projective geometry.

While emphasizing affine geometry and its basis in Euclidean concepts, the book.

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