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 Isomorphisms
2.4 Homogeneous Vectors
2.5 Projective Geometrics
2.6 The Embedding of Affine Geometry in Projective Geometry
2.7 The Fundamental Incidence Theorems of Projective 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 Mappings
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 Coilineations
Solutions
List of Symbols
Bibliography
Index
