Linear algebra via exterior products
by Sergei Winitzki
Publisher: Ludwig-Maximilians University 2009
Number of pages: 82
Description:
A pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the elementary array-based formalism of vector and matrix calculations. In this book, the author makes extensive use of the exterior product of vectors. He shows how the standard properties of determinants, the Liouville formula, the Hamilton-Cayley theorem, and Pfaffians, as well as some results concerning eigenspace projectors can be derived without cumbersome matrix calculations.
Download or read it online for free here:
Download link
(1.6MB, PDF)
Similar books
Grassmann Algebraby John Browne
The primary focus of this book is to provide a readable account in modern notation of Grassmann's major algebraic contributions to mathematics and science. It should be accessible to scientists and engineers, students and professionals alike.
(17170 views)
An Introduction to Determinantsby William Thomson
Every important principle has been illustrated by copious examples, a considerable number of which have been fully worked out. As my main object has been to produce a textbook suitable for beginners, many important theorems have been omitted.
(7315 views)
Introduction to Linear Bialgebraby W.B.V. Kandasamy, F. Smarandache, K. Ilanthenral - arXiv
This book introduced a new algebraic structure called linear bialgebra. We have ventured in this book to introduce new concepts like linear bialgebra and Smarandache neutrosophic linear bialgebra and also give the applications of these structures.
(12708 views)
Linear Algebra, Infinite Dimensions, and Mapleby James V. Herod - Georgia Tech
These notes are about linear operators on Hilbert Spaces. The text is an attempt to provide a way to understand the ideas without the students already having the mathematical maturity that a good undergraduate analysis course could provide.
(14141 views)