Back Tensorverjüngung German Contracción tensorial Spanish Contraction tensorielle French Contrazione di un tensore Italian テンソルの縮約 Japanese Свёртка тензора Russian Згортка тензора Ukrainian
In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. In components, it is expressed as a sum of products of scalar components of the tensor(s) caused by applying the summation convention to a pair of dummy indices that are bound to each other in an expression. The contraction of a single mixed tensor occurs when a pair of literal indices (one a subscript, the other a superscript) of the tensor are set equal to each other and summed over. In Einstein notation this summation is built into the notation. The result is another tensor with order reduced by 2.
Tensor contraction can be seen as a generalization of the trace.