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Multilinear Algebra Werner H. Greub
Publisher: Springer

I've been weeding through some multilinear algebra and abstract algebra with respect to modules (more or less, vector spaces over rings), and tensors (products of modules, in which the product space is a module). (2) Volume 44, Number 4 (1992), 471-521, euclid. The exterior algebra Λ V \Lambda V of a vector space is the free graded-commutative algebra? Jul 9, 2013 - Abstract: Mathematical operators whose transformation rules constitute the building blocks of a multi-linear algebra are widely used in physics and engineering applications where they are very often represented as tensors. Over V V , where the elements of V V are taken to be of degree 1 1 . Thus most of the approaches to quantum flag varieties, define the quantum flag variety via its noncommutative graded algebra of functions (cf. 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. 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. Dec 2, 2012 - Linear and multilinear algebra, Matrix analysis, Horn, Johnson. Associative rings and algebras, Hopf algebras and their actions on rings, Montgomery. Quantum multilinear algebra, Mitsuyasu Hashimoto and Takahiro Hayashi Source: Tohoku Math. Oct 8, 2011 - Usual flag varieties are projective varieties, hence they have a (commutative) graded coordinate ring. I have a good background in linear algebra and some real analysis, but I am not interested in tensors as a purely mathematical construct, but for applications in mechanics. Nonassociative rings and algebras, Infinite-dimensional Lie algebras, Kac.