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
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