线性几何

线性几何，ISBN：9787510005411，作者：（德）格伦伯格 著

Guide to the Reader Chapter Ⅰ Vector Spaces 1. 1 Sets 1. 2 Groups. Fields and Vector Spaces 1. 3 Subspaces 1. 4 Dimension 1. 5 The Ground Field Chapter Ⅱ Affine and Projective Geometry 2. 1 Affine Geometries 2. 2 Affine Propositions of Incidence 2. 3 Affine lsomorphisms 2. 4 Homogeneous Vectors 2. 5 Projective Geometries 2. 6 Thc Embedding of Affine Geometry in Projective Geometry 2. 7 The Fundamental Incidence Theorems of pojective Geometry Chapter Ⅲ Isomorphisms 3. 1 Affinities 3. 2 Projectivities 3. 3 Linear Equations 3. 4 Affine and Projective Isomorphisms 3. 5 Semi－linear Isomorphisms 3. 6 Groups of Automorphisms 3. 7 Central Collineations Chapter Ⅳ Linear M appings 4. 1 Elementary Properties of Linear Mappings 4. 2 Degenerate Affinities and Projectivities 4. 3 Matrices 4. 4 The Rank of a Linear Mapping 4. 5 Linear Equations 4. 6 Dual Spaces 4. 7 Dualities 4. 8 Dual Geometries Chapter Ⅴ Bilinear Forms 5. 1 Elementary Properties of Bilinear Forms 5. 2 Orthogonality 5. 3 Symmetric and Alternating Bilinear Forms 5. 4 Structure Theorems 5. 5 Correlations 5. 6 Projective Quadrics 5. 7 Affine Quadrics 5. 8 Sesquilinear Forms Chapter Ⅵ Euclidean Geometry 6. 1 Distances and Euclidean Geometries 6. 2 Similarity Euclidean Geometries 6. 3 Euclidean Quadrics 6. 4 Euclidean Automorphisms 6. 5 Hilbert Spaces Chapter Ⅶ Modules 7. 1 Rings and Modules 7. 2 Submodules and Homomorphisms 7. 3 Direct Decompositions 7. 4 Equivalence of Matrices over F[x] 7. 5 Similarity of Matrices over F 7. 6 Classification of Collineations Solutions List of Symbols Bibliography Index