Linear algebra via exterior products
by Sergei Winitzki
Publisher: Ludwig-Maximilians University 2009
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.
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by W. B. V. Kandasamy, F. Smarandache - 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.
by G. Donald Allen - 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.
by 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.
by Robert Forsyth Scott - Cambridge University Press
In the present treatise I have attempted to give an exposition of the Theory of Determinants and their more important applications. The treatise uses Grassmann's alternate units, by means of which the study of determinants is much simplified.