Linear Algebra and Geometry

封面
Hong Kong University Press, 1974年1月1日 - 320 頁
Linear algebra is now included in the undergraduate curriculum of most universities. It is generally recognized that this branch of algebra, being less abstract and directly motivated by geometry, is easier to understand than some other branches and that because of the wide applications it should be taught as soon as possible. This book is an extension of the lecture notes for a course in algebra and geometry for first-year undergraduates of mathematics and physical sciences. Except for some rudimentary knowledge in the language of set theory the prerequisites for using the main part of the book do not go beyond form VI level. Since it is intended for use by beginners, much care is taken to explain new theories by building up from intuitive ideas and by many illustrative examples, though the general level of presentation is thoroughly axiomatic. Another feature of the book for the more capable students is the introduction of the language and ideas of category theory through which a deeper understanding of linear algebra can be achieved.
 

內容

Ch I LINEAR SPACE
1
Ch II LINEAR TRANSFORMATIONS
45
Ch III AFFINE GEOMETRY
96
Ch IV PROJECTIVE GEOMETRY
118
Ch V MATRICES
155
Ch VI MULTILINEAR FORMS
196
Ch VII EIGENVALUES
230
Ch VIII INNER PRODUCT SPACES
267
Index
306
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