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 - CuArt
Special Set Linear Algebras introduced by the authors in this free book is an extension of Set Linear Algebras, which are the most generalized form of linear algebras. These structures can be applied to multi-expert models.
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This book presents the basics of vector and tensor analysis for science and engineering students. Volume 1 covers algebraic structures and a modern introduction to the algebra of vectors and tensors. Clear presentation of mathematical concepts.
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