Vectors, Matrices and GeometryHong Kong University Press, 1994年8月1日 - 356 頁 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). |
內容
1 | |
39 | |
Ch 3 Conic sections | 89 |
Ch 4 Quadric surfaces | 167 |
Ch 5 Higher dimensional vector spaces | 207 |
Ch 6 Matrix and determinant | 243 |
Ch 7 Linear equations | 281 |
Numerical answers to exercises | 315 |
Index | 341 |
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常見字詞
a₁ algebraic angle asymptotes augmented matrix Ax² b₁ called coefficient matrix collinear column transformations column vectors complex numbers components cone conic coordinate axes coordinate planes Cramer's rule cross product curve cylinder defined denoted dependent directrix displacement vector distance dot product elementary row transformations ellipse ellipsoid example Exercise Find the equation foci following theorem geometry hyperbola hyperboloid invertible linear combination linear equations linearly independent linearly independent vectors major axis minor axis n-matrix non-zero vector obtain origin orthogonal pair parabola parabola y² perpendicular plane section position vectors proof Prove quadratic equation quadric surfaces r₁ real numbers rotation row rank row vectors scalar multiple Show Similarly solution square matrix standard position straight line subspace system of linear tangent THEOREM Let triangle unit coordinate vectors vector space R³ vectors X1 vertex x-axis x₁ xy-plane y-axis z-axis