Linear algebra via exterior products

Linear algebra via exterior products

Publisher: Ludwig-Maximilians University
Number of pages: 82

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.

Home page url

Download or read it online for free here:
Download link
(1.6MB, PDF)

Similar books

Book cover: Linear Algebra, Infinite Dimensions, and MapleLinear Algebra, Infinite Dimensions, and Maple
by - 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.
Book cover: n-Linear Algebra of Type I and Its Applicationsn-Linear Algebra of Type I and Its Applications
by - InfoLearnQuest
n-Linear Algebra of type I introduced in this book finds applications in Markov chains and Leontief economic models. Scientists and engineers can adopt this concept in fuzzy finite element analysis of mechanical structures with uncertain parameters.
Book cover: The Hermitian Two Matrix Model with an Even Quartic PotentialThe Hermitian Two Matrix Model with an Even Quartic Potential
by - American Mathematical Society
The authors consider the two matrix model with an even quartic potential and an even polynomial potential. The main result is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices.
Book cover: Lectures on Linear Algebra and MatricesLectures on Linear Algebra and Matrices
by - Texas A&M University
Contents: Vectors and Vector Spaces; Matrices and Linear Algebra; Eigenvalues and Eigenvectors; Unitary Matrices; Hermitian Theory; Normal Matrices; Factorization Theorems; Jordan Normal Form; Hermitian and Symmetric Matrices; Nonnegative Matrices.