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Built-in Mathematica Symbol

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Inner

Inner[f, list₁, list₂, g]
is a generalization of Dot in which f plays the role of multiplication and g of addition.

MORE INFORMATION

Inner[f, {{a, b}, {c, d}}, {x, y}, g]{g[f[a, x], f[b, y]], g[f[c, x], f[d, y]]}.

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 r tensor and a rank s tensor gives a rank tensor.

Inner[f, list₁, list₂] uses Plus for g.

Inner[f, list₁, list₂, g, n] contracts index n of the first tensor with the first index of the second tensor.

The heads of list₁ and list₂ must be the same, but need not necessarily be List. »

Basic Examples (3)

Compute the "inner f" of two lists, with "plus operation" g:

Compute a generalized inner product of a matrix and a vector:

Use familiar operations:

Generalizations & Extensions (2)

Applications (3)

Properties & Relations (2)

Outer Dot Thread MapThread ListCorrelate

Structural Operations

Tensors

Applying Functions to Lists

Tensors

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