Linear algebra via exterior products

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Linear algebra via exterior products

Linear algebra via exterior products

Name: Linear algebra via exterior products
ISBN: 9781409294962

Sergei Winitzki

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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.

الفئات:

Mathematics

عام:

2010

الناشر:

lulu.com

اللغة:

english

الصفحات:

285

ISBN 10:

140929496X