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This semester I'm taking a course in linear algebra and now at the end of the course we came to study the tensor product and multilinear algebra in general. I've already studied this theme in the past through Kostrikin's "Linear Algebra and Geometry", but I'm not sure this is enough.

My teacher didn't know what to recommend as textbook for this part of the course and he could just recommend one book that does everything in modules. Now, it's not that I'm not interested in modules, it's just that until today I've never dealt with them, so it's a little confusing to study the tensor product on that book.

In that case, what's a good reference to study multilinear algebra done in vector spaces? Is Kostrikin's book enough, or should I get other book to study this?

Thanks very much in advance!

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  • $\begingroup$ I like the introduction Munkres gives in his "Analysis on Manifolds". It is written in plain language accessible to undergrads. $\endgroup$ – Ragib Zaman Nov 6 '13 at 0:48
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I recommend Greub's book. It has excellent coverage of the subject and does not cost the gross national product of some small country.

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  • $\begingroup$ +1) Greub's book is great! It contains a lot of interesting morphisms, as well. $\endgroup$ – Avitus Nov 7 '13 at 12:48
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The first two chapters of "Tensors: Geometry and Applications" by Landsberg, for inspiration.

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A. Iozzi, Multilinear Algebra and Applications. Concise (100 pages), very clear explanation.

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For basic introduction, I strongly recommend Chern's "Lecture on Differential Geometry". I think it really inspiring. For extension, you may be interested in Clifford or geometric algebra which extends (multi-)linear algebra and everything doesn't care about its coordinate. Then Hestenes's book is quite appropriate.

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Here is a collection of good books on linear algebra and there is one on multilinear algebra as well. HTH

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  • $\begingroup$ The multilinear algebra book listed here is Greub's, given in another answer. $\endgroup$ – Joshua Grochow May 29 at 4:02

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