ENGLISH

Linear Algebra via Exterior Products

By Sergei Winitzki

Book information

Publisher
Lulu.com
Year
2010
ISBN
140929496X, 9781409294962
Language
english
Format
PDF
Filesize
2 MB (2510489 bytes)
Pages
299\299
Topic
Mathematics Algebra
Time added
2010-02-18 13:16:04

Description

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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