Vectors, Matrices and Geometry

This book is the last volume of a three-book series written for Sixth Form students and first-year undergraduates. It introduces the important concepts of finite-dimensional vector spaces through the careful study of Euclidean geometry. In turn, methods of linear algebra are then used in the study of coordinate transformations through which a complete classification of conic sections and quadric surfaces is obtained. The book concludes with a detailed treatment of linear equations in n variables in the language of vectors and matrices. Illustrative examples are included in the main text and numerous exercises are given in each section. The other books in the series are Fundamental Concepts of Mathematics (published 1988) and Polynomials and Equations (published 1992).

Kam-Tim Leung took his doctorate in mathematics in 1957 at the University of Zurich. During 1958-60, he taught at the Miami University and the University of Cincinnati. Since 1960 he has been a Senior Lecturer in Mathematics at The University of Hong Kong. His many publications include Elementary Set Theory, Linear Algebra and Geometry, Fundamental Concepts of Mathematics and Polynomials and Equations, all published by the Hong Kong University Press. He is also the main author of Basic Mathematics, a five-volume textbook for local secondary schools. Suk-Nam Suen took his Bachelor degree in Arts in 1985 at The University of Hong Kong, where he later obtained the Cert. Ed. He has been teaching mathematics since 1986, and is now Head of Mathematics and the Career Master at Tsang Pik Shan Secondary School.