The interior product is a dual notion of the wedge product in an exterior algebra 
, where 
is a vector space. Given an
orthonormal basis 
of 
, the forms
 |
(1)
|
are an orthonormal basis for 
. They define a metric on the exterior
algebra, 
.
The interior product with a form 
is the adjoint operator
of the wedge product with 
. That is,
 |
(2)
|
for all 
. For example,
 |
(3)
|
and
 |
(4)
|
where the 
are orthonormal, are two interior products.
For finite-dimensional real vector spaces, an inner product on 
gives an isomorphism 
with the dual
vector space 
.
The interior product is the composition of
this isomorphism with tensor
contraction.
