【内容提要】
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.本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.
【目 录】
Chapter 1VECTORS IN THE PLANE AND IN SPACF//l
Chapter 2 SUBSET，PRODLCTSET，RELATION AND MAPPINC//4
Chapter 3 THE n-DIMENSIONAL VECTORSPACE Vm//8
Chapter 4 THE PARAMETRIC REPRESENT ATIONOF A LINE//12
Chapter 5 SOME FUNDAMENTAL THEOREMS//19
Chapter 6 FIRST DEGREE FUNCTIONS ON，AND LINEARVARIETIES IN An//28
Chapter 7 LINEAR FUNCTIONS AND LINES IN A2 AND An APPLICATIONS//35
Chapter8 AFINITE AFFINE PLANE//47
Chapter 9 HOMOMORPHISMS OF VECTORSPACES//51
Chapter 10 MATRICES//62
Chapter 11 SETS OF LINEAR EQLATIONS//71
Chapter 12 FUNCTIONS OF SEVERAL VARIABLESDETERMINANT//75
Chapter 13 APPLICATIONS OF DETERMINANTSVOLUME//86
Chapter 14 QUADRATIC AND SYMMETRICBILINEAR FUNCTIONS//93
Chapter 15 EUCLIDEAN SPACE//113
Chapter 16 SOME APPLICATIONS INSTATISTICS//127
Chapter 17 CLASSIFICATION OFENDOMORPHISMS//138
Chapter 18 QUADRATIC FUNCTIONS ON AND QUADRATIC VARIETIESIN EUCLIDEAN SPACES//158
Chapter 19 MOTIONS AND AFFINITIES//168
Chapter 20 PROJECTIVE GEOMETRY//184
Chapter 21 NON-EUCLIDEAN PLANES//209
Chapter 22 SOME TOPOLOGICALREMARKS//219
Chapter 23 HINTS AND ANSWERS TO THEPROBLEMS IN CHAPTER 3-21//226