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Reference.org
Alternating multilinear map
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, more specifically in <a href="/facts/Multilinear_algebra/LrwpUFsM">multilinear algebra</a>, an alternating multilinear map is a <a href="/facts/Multilinear_map/YosSfBKE">multilinear map</a> with all arguments belonging to the same vector space (for example, a <a href="/facts/Bilinear_form/gyvzn9ym">bilinear form</a> or a <a href="/facts/Multilinear_form/Rk420AcK">multilinear form</a>) that is zero whenever any pair of its arguments is equal. This generalizes directly to a <a href="/facts/Module_(mathematics)/jP0LIhFL">module</a> over a <a href="/facts/Commutative_ring/QS1r2ovR">commutative ring</a>. </p><p>The notion of alternatization (or alternatisation) is used to derive an alternating multilinear map from any multilinear map of which all arguments belong to the same space. </p>