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of ), . Note that linear functionals (multilinear 1-forms over ) are trivially alternating, so that , while, by convention, 0-forms are defined to be scalars: .

The determinant on matrices, viewed as an argument function of the column vectors, is an important example of an alternating multilinear form.

Exterior product

The tensor product of alternating multilinear forms is, in general, no longer alternating. However, by summing over

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