Do you know any good reference on multilinear algebra?
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, little-known even in France : Les Tenseurs, Hermann, 1998.
It is remarkably well written and contains a wealth of information not found, to my knowledge, in other books. The bad news : it is in French and not translated...
3) Finally there is an amazingly original free book by Sergei Winitzki , Linear Algebra via Exterior Products. Here is the link
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 in-depth treatment which also explains the universal properties of the symmetric, exterior, and tensor algebras along with other multilinear constructions.
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