Do you know any good reference on multilinear algebra?

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Linear Algebra by Hoffman and Kunze covers this in chapter 5, where the tensor and exterior algebras are introduced. Algebra by Serge Lang covers this in more detail in the later chapters, but this is a more difficult and indepth treatment which also explains the universal properties of the symmetric, exterior, and tensor algebras along with other multilinear constructions. 


Dear mingming, here are three excellent books. 1) Tensor Spaces and Exterior Algebra by Takeo Yokonuma. Translations of Mathematical Monographs, volume 108, AMS 1992 You can browse it in Google books here 2) Laurent Schwartz ( yes, the Fields medalist of distibutions fame) wrote a book, littleknown even in France : Les Tenseurs, Hermann, 1998. 3) Finally there is an amazingly original free book by Sergei Winitzki , Linear Algebra via Exterior Products. Here is the link 


For the tensor, exterior and symmetric algebras of a module over a commutative ring I suggest the notes by Murfet http://therisingsea.org/notes/TensorExteriorSymmetric.pdf 


The standard reference is Greub's Multilinear algebra. There's also the book by Northcott. 

