线性几何 : 第2版

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

《线性几何（第2版）（英文版）》内容为Vector Spaces、Sets、Groups. Fields and Vector Spaces、Subspaces、Dimension、The Ground Field、Affine and Projective Geometry、Affine Geometries、Affine Propositions of Incidence、Affine lsomorphisms、Homogeneous Vectors、Projective Geometries、The Embedding of Affine Geometry in Projective Geometry、The Fundamental Incidence Theorems of pojective Geometry、Isomorphisms、ffinities、Projectivities等等。