UID:
almahu_9947366319502882
Format:
1 online resource (327 p.)
ISBN:
1-281-76314-4
,
9786611763145
,
0-08-087310-3
Series Statement:
Pure and applied mathematics ; 2
Content:
Linear algebra and projective geometry
Note:
Description based upon print version of record.
,
Front Cover; Linear Algebra and Projective Geometry; Copyright Page; Preface; Contents; Chapter I. Motivation; I.1. The Three-Dimensional Affine Space as Prototype of Linear Manifolds; I.2. The Real Projective Plane as Prototype of the Lattice of Subspaces of a Linear Manifold; Chapter II. The Basic Properties of a Linear Manifold; II.1. Dedekind's Law and the Principle of Complementation; II.2. Linear Dependence and Independence; Rank; II.3. The Adjoint Space; Appendix I. Application to Systems of Linear Homogeneous Equations; Appendix II. Paired Spaces; II.4. The Adjunct Space
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Appendix III. Fano's PostulateChapter III. Projectivities; III.1. Representation of Projectivities by Semi-linear Transformations; Appendix I. Projective Construction of the Homothetic Group; III.2. The Group of Collineations; III.3. The Second Fundamental Theorem of Projective Geometry; Appendix II. The Theorem of Pappus; III.4. The Projective Geometry of a Line in Space; Cross Ratios; Appendix III. Projective Ordering of a Space; Chapter IV. Dualities; IV.1. Existence of Dualities; Semi-bilinear Forms; IV.2. Null Systems; IV.3. Representation of Polarities
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IV.4. Isotropic and Non-isotropic Subspaces of a Polarity Index and Nullity; Appendix I. Sylvester's Theorem of Inertia; Appendix II. Projective Relations between Lines Induced by Polarities; Appendix III. The Theorem of Pascal; IV.5. The Group of a Polarity; Appendix IV. The Polarities with Transitive Group; IV.6. The Non-isotropic Subspaces of a Polarity; Chapter V. The Ring of a Linear Manifold; V.1. Definition of the Endomorphism Ring; V.2. The Three Cornered Galois Theory; V.3. The Finitely Generated Ideals; V.4. The Isomorphisms of the Endomorphism Ring
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V.5. The Anti-isomorphisms of the Endomorphism RingAppendix I. The Two-sided Ideals of the Endomorphism Ring; Chapter VI. The Groups of a Linear Manifold; VI.1. The Center of the Full Linear Group; VI.2. First and Second Centralizer of an Involution; VI.3. Transformations of Class 2; VI.4. Cosets of Involutions; VI.5. The Isomorphisms of the Full Linear Group; Appendix I. Groups of Involutions; VI.6. Characterization of the Full Linear Group within the Group of Semi-linear Transformations; VI.7. The Isomorphisms of the Group of Semi-linear Transformations
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Chapter VII. Internal Characterization of the System of SubspacesA Short Bibliography of the Principles of Geometry; VII.1. Basic Concepts, Postulates and Elementary Properties; VII.2. Dependent and Independent Points; VII.3. The Theorem of Desargues; VII.4. The Imbedding Theorem; VII.5. The Group of a Hyperplane; VII.6. The Representation Theorem; VII.7. The Principles of Affine Geometry; Appendix S. A Survey of the Basic Concepts and Principles of the Theory of Sets; A Selection of Suitable Introductions into the Theory of Sets; Sets and Subsets; Mappings; Partially Ordered Sets
,
Well Ordering
,
English
Additional Edition:
ISBN 0-12-072250-X
Language:
English
