most recent 30 from http://mathoverflow.net 2013-05-24T13:03:50Z http://mathoverflow.net/feeds/question/17521 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17521/any-reference-on-multilinear-algebra mingming 2010-03-08T21:12:17Z 2012-06-06T15:47:52Z

<p>Do you know any good reference on multilinear algebra?</p>

http://mathoverflow.net/questions/17521/any-reference-on-multilinear-algebra/17528#17528 lhf 2010-03-08T21:34:54Z 2010-03-08T21:34:54Z

<p>The standard reference is Greub's <em>Multilinear algebra</em>. There's also the book by Northcott.</p>

http://mathoverflow.net/questions/17521/any-reference-on-multilinear-algebra/17529#17529 Harry Gindi 2010-03-08T21:35:15Z 2010-03-08T21:35:15Z

<p><em>Linear Algebra</em> by Hoffman and Kunze covers this in chapter 5, where the tensor and exterior algebras are introduced. <em>Algebra</em> 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.</p>

http://mathoverflow.net/questions/17521/any-reference-on-multilinear-algebra/17540#17540 Georges Elencwajg 2010-03-08T22:23:27Z 2010-03-08T22:23:27Z

<p>Dear mingming, here are three excellent books.</p> <p>1) <em>Tensor Spaces and Exterior Algebra</em> by Takeo Yokonuma. Translations of Mathematical Monographs, volume 108, AMS 1992</p> <p>You can browse it in Google books <a href="http://books.google.fr/books?id=sgmxKCFw7nIC&amp;printsec=frontcover&amp;dq=yokonuma&amp;source=bl&amp;ots=jCql_ZyXb7&amp;sig=PP1TRG97kPtQZcQEvBXv_zfbuIc&amp;hl=fr&amp;ei=xHGVS6WcG8PH4gblx5WEDQ&amp;sa=X&amp;oi=book_result&amp;ct=result&amp;resnum=3&amp;ved=0CA0Q6AEwAg#v=onepage&amp;q=&amp;f=false" rel="nofollow">here</a></p> <p>2) Laurent Schwartz ( yes, the Fields medalist of distibutions fame) wrote a book, little-known even in France : <em>Les Tenseurs</em>, Hermann, 1998.<br> 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...</p> <p>3) Finally there is an amazingly original free book by Sergei Winitzki , <em>Linear Algebra via Exterior Products</em>. Here is the <a href="http://sites.google.com/site/winitzki/linalg/Linear_algebra_exterior.pdf?attredirects=0&amp;d=1" rel="nofollow">link</a></p>

http://mathoverflow.net/questions/17521/any-reference-on-multilinear-algebra/17543#17543 babubba 2010-03-08T22:39:05Z 2010-03-08T22:39:05Z

<p>For the tensor, exterior and symmetric algebras of a module over a commutative ring I suggest the notes by Murfet <a href="http://therisingsea.org/notes/TensorExteriorSymmetric.pdf" rel="nofollow">http://therisingsea.org/notes/TensorExteriorSymmetric.pdf</a></p>