  Tensor decomposition plays a key role in identifying common features across a
collection of matrices in many areas of science. A fundamental need in big data
research is to process data tabulated as large-scale matrices using
eigenvectors. A higher order generalized singular value decomposition technique
successfully captures the common features of the same organ from multiple
animals in genomic signal processing. A recent semidefinite programming
approach to solve an AC optimal power flow was accompanied by the problem
formulation in the Cartesian coordinate system. The collection of nodal
Kirchhoff laws introduces a 3D tensor with a common feature of individual
matrices to maintain local power balance. In this paper, the mathematical
process is established and the common feature is identified. The common feature
is a key element to a fully decentralized and therefore scalable algorithm to
solve AC optimal power flow.
