Linear algebra via exterior products
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SMS Library | 512.64 WIN-L (Browse shelf(Opens below)) | Available | 25174 |
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512.64 STR-L Linear algebra and its applications | 512.64 VEN-E Elementary linear algebra | 512.64 WHI-L Linear and nonlinear waves | 512.64 WIN-L Linear algebra via exterior products | 512.64 YAN-A Concise text on advanced linear algebra(a) | 512.64 ZHA-P Problems in linear algebra and matrix theory | 512.642 BAT-T Theory of finite linear spaces (the): combinatorics of points and lines |
This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.
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