Linear algebra and projective geometry.
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Linear algebra and projective geometry.

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Published by Academic Press in New York .
Written in English

Subjects:

  • Geometry, Projective.,
  • Transformations (Mathematics)

Book details:

Edition Notes

Includes bibliography.

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

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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. ISBN , Book Edition: 1. Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michle 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.