Linear Algebra and Projective Geometry PDF Download
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Author: Reinhold Baer
Publisher: Courier Corporation
ISBN: 0486154661
Category : Mathematics
Languages : en
Pages : 338
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Book Description
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: Reinhold Baer
Publisher: Courier Corporation
ISBN: 0486154661
Category : Mathematics
Languages : en
Pages : 338
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Book Description
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: Ludwik Silberstein
Publisher:
ISBN:
Category : Vector algebra
Languages : en
Pages : 98
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Book Description
Author: Ludwik Silberstein
Publisher: Forgotten Books
ISBN: 9781330181966
Category : Mathematics
Languages : en
Pages : 86
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Book Description
Excerpt from Projective Vector Algebra: An Algebra of Vectors Independent of the Axioms of Congruence and of Parallels I. The reader will find in the widely known memoir of Hilbert on the Foundations of Geometry* various 'algebras of segments,' independent of one or of another group of axioms, the purpose of these algebras being, in Hilbert's case, to show the mutual independence of his set of axioms. More recently, in an excellent book, Schur has taken up von Staudt's calculus of projective segments (Wurfrechnung) in order to develop it analytically and to build upon it a complete system of metrical, euclidean and non-euclidean, geometry. This is admirably done in 4 and 5 of his work. Schur bases his definitions of equality, of addition and multiplication of projective segments, upon the correspondence known as 'prospectivity,' and, at first, avails himself only of the axioms of connection and of order [Schur's postulates I. to 8.]; for the further development of the subject, however, he has recourse [5] to the axioms of congruence or of 'motion,' postulates 9. to 13., and completes his investigation by adding an independent, 14th postulate concerning the use of compasses. The result is a most charming and lucid structure of the complete system of non-euclidean geometry (of an isotropic three-dimensional space of any constant curvature), the last touch to this true masterpiece being given in Schur's closing section by adding the archimedean postulate. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Christian Okonek
Publisher: Springer Science & Business Media
ISBN: 1475714602
Category : Mathematics
Languages : en
Pages : 399
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Book Description
These lecture notes are intended as an introduction to the methods of classification of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = Fn. According to Serre (GAGA) the classification of holomorphic vector bundles is equivalent to the classification of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some funda mental results from these fields are summarized at the beginning. One of the authors gave a survey in the Seminaire Bourbaki 1978 on the current state of the classification of holomorphic vector bundles overFn. This lecture then served as the basis for a course of lectures in Gottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the introductory nature of this book we have had to leave out some difficult topics such as the restriction theorem of Barth. As compensation we have appended to each sec tion a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of paragraphs. Each section is preceeded by a short description of iv its contents.
Author: Christian Okonek
Publisher: Springer Science & Business Media
ISBN: 3034801513
Category : Mathematics
Languages : en
Pages : 246
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Book Description
These lecture notes are intended as an introduction to the methods of classi?cation of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = P . According to Serre (GAGA) the class- n cation of holomorphic vector bundles is equivalent to the classi?cation of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some fundamental results from these ?elds are summarized at the beginning. One of the authors gave a survey in the S ́eminaire Bourbaki 1978 on the current state of the classi?cation of holomorphic vector bundles over P . This lecture then served as the basis for a course of lectures n in G ̈ottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the - troductory nature of this book we have had to leave out some di?cult topics such as the restriction theorem of Barth. As compensation we have appended to each section a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of pa- graphs. Each section is preceded by a short description of its contents.
Author: Ludwik Silberstein
Publisher: Forgotten Books
ISBN: 9780428948405
Category : Mathematics
Languages : en
Pages : 86
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Book Description
Excerpt from Projective Vector Algebra: An Algebra of Vectors Independent of the Axioms of Congruence and of Parallels These suffice for the full validity of Desargues' theorem, a theorem whose aid will be most essential. (readers who are unfamiliar with this fundamental theorem can look up its proof in Prof. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Lars Kadison
Publisher: Birkhäuser Boston
ISBN: 0817639004
Category : Mathematics
Languages : en
Pages : 228
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Book Description
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: Ludwik Silberstein
Publisher:
ISBN:
Category :
Languages : en
Pages : 78
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Book Description
Author: Alexander Kleshchev
Publisher: Cambridge University Press
ISBN: 1139444069
Category : Mathematics
Languages : en
Pages : 293
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Book Description
The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own
Author: Jürgen Richter-Gebert
Publisher: Springer Science & Business Media
ISBN: 3642172865
Category : Mathematics
Languages : en
Pages : 573
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Book Description
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.
