Main Page | See live article | Alphabetical index In mathematics, contraction has two meanings: See contraction mapping. Contraction of a tensor. It occurs when a pair of literal indices (one a subscript, the other a superscript) of a mixed tensor are set equal to each other so that a summation over that index takes place (due to the Einstein summation convention). The result is another tensor whose rank is reduced by 2. If a tensor is dyadic then its contraction is a scalar obtained by dotting each pair of base vectors in each dyad. E.g. Let be a dyadic tensor, then its contraction is , a scalar of rank 0. E.g. Let be a dyadic tensor. This tensor does not contract; if its base vectors are dotted the result is the contravariant metric tensor, , whose rank is 2. More generally, if V is a vector space over the field k and V* is its dual vector space, then the contraction is the linear transformation given by =a(b). References. Mathematical Physics by Donald H. Menzel. Dover Publications, New York. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.