Erschienen: 23.11.2009 Abbildung von Dodson / Poston | Tensor Geometry | 2nd ed. 1991. Corr. 3rd printing | 2009 | The Geometric Viewpoint and it... | 130

Dodson / Poston

Tensor Geometry

The Geometric Viewpoint and its Uses

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106,99 €

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2nd ed. 1991. Corr. 3rd printing 2009. Buch. xiv, 434 S. Bibliographien. Hardcover

Springer. ISBN 978-3-540-52018-4

Format (B x L): 15,5 x 23,5 cm

Gewicht: 884 g

In englischer Sprache

Das Werk ist Teil der Reihe: Graduate Texts in Mathematics; 130

Produktbeschreibung

We have been very encouraged by the reactions of students and teachers using our book over the past ten years and so this is a complete retype in TEX, with corrections of known errors and the addition of a supplementary bibliography. Thanks are due to the Springer staff in Heidelberg for their enthusiastic sup­ port and to the typist, Armin Kollner for the excellence of the final result. Once again, it has been achieved with the authors in yet two other countries. November 1990 Kit Dodson Toronto, Canada Tim Poston Pohang, Korea Contents Introduction. XI O. Fundamental Not(at)ions. 1 1. Sets. 1 2. Functions. 6 3. Physical Background. 13 I. Real Vector Spaces. 18 1. Spaces. 18 Subspace geometry, components 2. Maps. 24 Linearity, singularity, matrices 3. Operators. 31 Projections, eigenvalues, determinant, trace II. Affine Spaces. 43 1. Spaces. 43 Tangent vectors, parallelism, coordinates 2. Combinations of Points. 49 Midpoints, convexity 3. Maps. 53 Linear parts, translations, components III. Dual Spaces. 57 1. Contours, Co- and Contravariance, Dual Basis. 57 IV. Metric Vector Spaces. 64 1. Metrics. 64 Basic geometry and examples, Lorentz geometry 2. Maps. 76 Isometries, orthogonal projections and complements, adjoints 3. Coordinates. 83 Orthonormal bases Contents VIII 4. Diagonalising Symmetric Operators 92 Principal directions, isotropy V. Tensors and Multilinear Forms 98 1. Multilinear Forms. 98 Tensor Products, Degree, Contraction, Raising Indices VE Topological Vector Spaces. 114 1. Continuity. 114 Metrics, topologies, homeomorphisms 2. Limits. 125 Convergence and continuity 3. The Usual Topology.

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