Affine Maps, Euclidean Motions and Quadrics

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Affine geometry and quadric are fascinating subjects alone, but they are also important applications of linear algebra. They give a first glimpse into the world of algebraic geometry yet they are equally relevant to a wide range ofdisciplines such as engineering. This text discusses and classifies affinities and Euclidean motions culminating in classification results for quadric. A high level of detail and generality is a key feature unmatched by other books available. Such intricacy makes this a particularly accessible teaching resource as it requires no extra time in deconstruction the author’s reasoning. The provision of a large number of exercises with hints will help students to develop their problem solving skills and will also be a useful resource for lecturers when setting work for independent study. Affinities, Euclidean Motions and Quadric takes rudimentary, and often taken-for-granted, knowledge and presents it in a new, comprehensive form. Standard and non-standard examples are demonstrated throughout and an appendix provides the reader with a summary of advanced linear algebra facts for quick reference to the text. All factors combined, this is a self-contained book ideal for self-study that is not only foundational but unique in its approach.’ This text will be of use to lecturers in linear algebra and its applications to geometry as well as advanced undergraduate and beginning graduate students. Table of Contents 1 Affine Spaces 2 Affinities 3 Classification of Affinities 4 Classification of Affinities in Arbitrary Dimension 5 Euclidean Affine Spaces 6 Euclidean Motions 7 Euclidean Motions of the Line, the Plane and of Space 8 Affine Classification of Real Quadric 9 Orthogonal Classification of Quadric A Vector Spaces with Scalar Product B Diagonalization of Bilinear Symmetric Maps C Orthogonal Diagonalization D Polynomials with the Same Zeros Bibliography Author Index Subject Index