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Inner

FilledSmallSquare Inner[f, , , g] is a generalization of Dot in which f plays the role of multiplication and g of addition.

FilledSmallSquare Example: Inner[f,a,b,x,y,g] LongRightArrow.

FilledSmallSquare Inner[f,a,b,c,d,x,y,g] LongRightArrow.

FilledSmallSquare Like Dot, Inner effectively contracts the last index of the first tensor with the first index of the second tensor. Applying Inner to a rank tensor and a rank tensor gives a rank tensor.

FilledSmallSquare Inner[f, , ] uses Plus for g.

FilledSmallSquare Inner[f, , , g, n] contracts index n of the first tensor with the first index of the second tensor.

FilledSmallSquare The heads of and must be the same, but need not necessarily be List.

FilledSmallSquare See Section 2.2.10 and Section 3.7.11.

FilledSmallSquare See also: Outer, Thread, MapThread, ListCorrelate.

FilledSmallSquare New in Version 1.

Further Examples