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SequenceOuter (modified)

Cross

FilledSmallSquareCross[a, b] gives the vector cross product of a and b.

FilledSmallSquare If a and b are lists of length 3, corresponding to vectors in three dimensions, then Cross[a, b] is also a list of length 3.

FilledSmallSquareCross[a, b] can be entered in StandardForm and InputForm as a b, a AliasIndicatorcrossAliasIndicator b or a \[Cross] b. Note the difference between \[Cross] and \[Times].

FilledSmallSquareCross is antisymmetric, so that Cross[b, a] is -Cross[a, b].

FilledSmallSquare In general, Cross[, , ... , ] is a totally antisymmetric product which takes vectors of length n and yields a vector of length n that is orthogonal to all of the .

FilledSmallSquareCross[, , ... ] gives the dual (Hodge star) of the wedge product of the , viewed as one-forms in dimensions.

FilledSmallSquare See The Mathematica Book: Section 1.8.3.

FilledSmallSquare See also: Dot, Signature, Outer.

Further Examples

SequenceOuter (modified)