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線性幾何（簡體書）
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ISBN13：9787510005411
出版社：世界圖書(北京)出版公司
作者：(德)格倫伯格
出版日：2009/10/01
裝訂／頁數：平裝／198頁
規格：19cm*13cm (高/寬)
版次：2
人民幣定價：28 元
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《線性幾何(第2版)(英文版)》內容簡介：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。
目次
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
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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