Built-in Mathematica Symbol

Inner

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

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, 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. »

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:

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:

Generalized inner product of two matrices:

Inner product of a matrix with a vector:

Inner product of a vector with a matrix:

Contract over the first index of the first matrix:

Inner works with heads other than List:

The divergence of a vector field is an inner differentiation:

Inner product of two Boolean matrices:

Applying the functions in a list to corresponding arguments:

This gives the scalar product of two vectors:

This does the same thing:

Combining the products with List gives the same result as MapThread: