tensor contraction


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tensor contraction

[′ten·sər kən′trak·shən]
(mathematics)
For a tensor having an upper and a lower index, summation over the components in which these indexes have the same value, in order to obtain a new tensor two lower in rank.
References in periodicals archive ?
This time-consuming task stands to be transformed now by a novel software, the Tensor Contraction Engine (TCE), developed by a consortium led by Ponnuswamy Sadayappan at Ohio State Univ., Columbus.
The vector [mathematical expression not reproducible] 1 can be cheaply computed by tensor contractions. After (2.6) has been solved, the TT format of the tensor X is updated by reshaping gk into its kth TT core.
Hence, the correct interpretation above is to first expand the summation over combinations and then enforce the tensor contractions for each term separately.