Leung K.T., Sven S.N. Vectors, Matrices and Geometry

Hong Kong University Press, 1995. - 356 pages.With the present volume the 3-book series on elementary mathematics is now complete. Like its two predecessors, Fundamental Concepts of Mathematics and Polynomials and Equations, the present book is addressed to a large leadership comprising Sixth Form students, first-year undergraduates and students of Institutes of Education.
In Chapter One vectors in the plane arc simply defined as ordered pairs of their components. Their addition and scalar multiplication are accordingly given in terms of their components. As soon as the fundamental properties of these operations are established our treatment of the linear algebra of R2 becomes increasingly independent of the use of components, and the majority of the theorems are seen as logical consequences of the said fundamental properties. Important ideas of linear algebra are then introduced in the context of the familiar plane geometry. In turn the newly obtained methods of linear algebra are used to explore some less familiar areas of plane geometry.