线性代数与几何（英文版） / 国外优秀数学著作原版系列
作者： (荷)凯珀
出版时间：2016年6月
出版社：哈尔滨工业大学出版社
- 哈尔滨工业大学出版社
- 9787560358932
- 137984
- 2016年6月
- 未分类
- 未分类
- O151.2
线性代数几何包括分析几何、仿射几何和射影几何等。在本科目中线性代数占主要地位，因为本科目的实质是线性代数。由荷兰凯珀所著的《线性代数与几何（英文版）／国外优秀数学著作原版系列》一书试图洞察作为现代代数工具的线性代数在数学中的作用。本书包括一些几何理论、初级和重要的代数概念和理论，如：向量平面、向量空间、矩阵、欧几里得空间、射影几何等内容。
本书可供高等院校本科生、研究生及数学研究人员参考阅读。
Chapter 1 VECTORS IN THE PLANE AND IN SPACE
Chapter 2 SUBSET，PRODUCT SET，RELATION AND MAPPING
Chapter 3 THE n-DIMENSIONAL VECTOR SPACE Vn
Chapter 4 THE PARAMETRIC REPRESENTATION OF A LINE
Chapter 5 SOME FUNDAMENTAL THEOREMS
The dual vector space V*
Chapter 6 FIRST DEGREE FUNCTIONS ON，AND LINEAR VARI-ETIES IN An
Chapter 7 LINEAR FUNCTIONS AND LINES IN A2 AND An APPLI-CATIONS
Cross-ration
Harmonic separation
Chapter 8 A FINITE AFFINE PLANE
Chapter 9 HOMOMORPHISMS OF VECTOR SPACES
The vector space Hom（A，B）
Composition（multiplication）of homomorphisms
The dual homomorphism of the dual vector spaces
Chapter 10 MATRICES
Chapter 11 SETS OF LINEAR EQUATIONS
Chapter 12 FUNCTIONS OF SEⅦRAL VARIABLES DETERMINANT
Chapter 13 APPLICATIONS OF DETERMINANTS VOLUME
Chapter 14 QUADRATIC AND SYMMETRIC BILINEAR FUNCTIONS
A．Functions on a vector space
AH．Hermitian functions
B．Functions on a real affine space
Chapter 15 EUCLIDEAN SPACE
Unitary vector space
Chapter 16 SOME APPLICATIONS IN STATISTICS
Method of least squares，linear adjustment，regression
The correlation coefficient
Chapter 17 CLASSIFICATION OF ENDOMORPHISMS
Classification of endomorphisms（complex numbers）
Endomorphisms of real vector spaces
Symmetric endomorphisms and quadratic functions on a Euclidean vector space
Orthogonal endomorphisms
Hermitian endomorphisms and hermitian functions on a unitary space
Chapter 18 QUADRATIC FUNCTIONS ON AND QUADRATIC VARIETIES IN EUCLIDEAN SPACES
Investigation of a given quadratic variety
Chapter 19 MOTIONS AND AFFINITIES
Motions
Classification of motions
Morion in the euclidean plane as basic notion
Affinities in real spaces
Some constructions with plane affinities
Chapter 20 PROJECTIVE GEOMETRY
Points at infinity of an affiBe plane A2
Projective classification of quadrics（over C and R）
Classification of collineations（over C and R）
Chapter 21 NON—EUCLIDEAN PLANES
The hyperbolic plane
The elliptic plane
Chapter 22 SOME TOPOLOGICAL REMARKS
Chapter 23 HINTS AND ANSWERS TO THE PROBLEMS IN CHAPTERS 3-21
