The term triple dot product has distinct meanings in vector and tensor notation. An ordinary dot product is a binary
operation that maps two vectors to a scalar,
so a dot product of three vectors is not defined by associating
the symbols as 
:
this would attempt to take the dot product of a scalar and a vector.
In vector algebra, "triple dot product" is sometimes used informally for the scalar triple product
![a·[b×c],](/images/equations/TripleDotProduct/NumberedEquation1.svg) |
which uses one cross product and one dot product, not three dot products.
In tensor analysis, a triple dot denotes contraction over three pairs of indices. For third-rank tensors 
and 
with components 
and 
, one convention gives the scalar
 |
(Verscharen et al. 2019). This is a tensor contraction of two tensors, not a product of three vectors.
