Linear Algebra via Exterior Products by Sergei Winitzki
Linear Algebra via Exterior Products - Table of Contents
0. Introduction and summary
1. Linear algebra without coordinates
2.. Exterior product
3. Basic applications
4. Advanced applications
5. Scalar product
A. Complex numbers
B. Permutations
C. Matrices
D. Distribution of this text
What You Will Learn in Linear Algebra via Exterior Products
This text introduce 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. It introduces a new way of looking at linear algebra using exterior products, which help understand higher-dimensional spaces. The book explains the geometric and algebraic ideas behind vector spaces and connects them to real-world problems in fields like physics and engineering. It 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. It’s great for students who already know basic linear algebra and want to dive into more advanced topics.
Book Details & Specifications
Title:
Linear Algebra via Exterior Products by Sergei Winitzki
Publisher:
Ludwig-Maximilians University
Year:
2009
Pages:
285
Type:
PDF
Language:
English
ISBN-10 #:
140929496X
ISBN-13 #:
978-1409294962
License:
GNU
Amazon:
Amazon
About the Author: Sergei Winitzki
The author Sergei Winitzki
is a mathematician who wrote Linear Algebra via Exterior Products, where he takes a different approach to linear algebra. Instead of just using traditional methods like matrices, he focuses on exterior products, which help explain concepts like determinants and geometry, such as volume and orientation.
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