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, K. Ilanthenral - InfoLearnQuest
Set linear algebras, introduced by the authors in this book, are the most generalized form of linear algebras. These structures make use of very few algebraic operations and are easily accessible to non-mathematicians as well.
by 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.
by Peter J. Cameron - Queen Mary, University of London
On the theoretical side, we deal with vector spaces, linear maps, and bilinear forms. On the practical side, the subject is really about one thing: matrices. This module is a mixture of abstract theory and concrete calculations with 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.