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For a brief explanation of the geometric meaning of exterior product, inner interior product of a k-form and l-vector, Hodge dual etc. see my answer here: http://mathoverflow.net/questions/4648/when-to-pick-a-basis/4900#4900

The best reference for this stuff is Bourbaki, Algebra, Chapter 3.

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For a brief explanation of the geometric meaning of exterior product, inner product of a k-form and l-vector, Hodge dual etc. see my answer here: http://mathoverflow.net/questions/4648/when-to-pick-a-basis/4900#4900

The best reference for this stuff is Bourbaki, Algebra, Chapter 3.