# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Inner

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

## DetailsDetails

• 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 and must be the same, but need not necessarily be List. »

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

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

 Out[1]=

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

 Out[1]=

Use familiar operations:

 Out[1]=
 Out[2]=