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Multilinear Algebra Werner H. Greub
Publisher: Springer

Nov 11, 2013 - I know linear algebra at a graduate level (from engineering courses, not from mathematics courses), but I cannot find anything that transitions to multilinear algebra. And tensor algebra are very new concepts to me and I want to understand how to prove the following property of the wedge product: $$\omega\wedge(\eta_{1}+\eta_{2})=\omega\wedge\eta_{1}+\omega\wedge\eta_{2}$$. Let 𝔤 \mathfrak{g} be a degreewise finite-dimensional ℕ + \mathbb{N}_+ graded vector space equipped with multilinear graded-symmetric maps. " I tried to start reading Representation theory, by Fulton and Harris with nothing more than an undergraduate abstract algebra introduction as preparation. Jun 14, 2011 - To appear in Linear and Multilinear Algebra (2011). E-print: arXiv:1008.3633 [quant-ph]; L. Beasley, Linear operators on matrices: the invariance of rank k matrices. Equivalently a dg-algebra-structure on ∧ • 𝔤 * \wedge^\bullet \mathfrak{g}^* . Jun 13, 2007 - So one learns early enough about spectral theorem, polar decomposition, and determinants which are defined using the exterior algebra and volume forms. It does not cover much in multilinear algebra though. Linear Algebra and its Applications 107, 161–167 (1988). Feb 3, 2014 - For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation principle essential to study tensors, including a big amount of workout routines. May 8, 2010 - Multilinear algebra has important applications in many different areas of mathematics but is usually learned in a rather haphazard fashion. Linear and Multilinear Algebra. Jan 25, 2013 - This is pretty trivial example but if you imagine higher dimensional objects, tracking indices would be cumbersome so multi-linear algebra makes life easy. Apr 21, 2014 - 2- Fuad Kittaneh, Yousef Manasrah, Revereses Young and Heinz Inequalities for Matrices. Feb 17, 2007 - This happened with dual spaces and multilinear algebra.