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Linear Algebra via Exterior Products

BySergei 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.

Details

Publication Date
Jul 30, 2009
Language
English
ISBN
9781409294962
Category
Science & Medicine
Copyright
Some Rights Reserved - Creative Commons (CC BY)
Contributors
By (author): Sergei Winitzki

Specifications

Pages
285
Binding
Perfect Bound
Interior Color
Black & White
Dimensions
US Trade (6 x 9 in / 152 x 229 mm)

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