First Degree Rectangular Eigenvalue Problems of Cubic Arrays Over Two Dimensional Ways: A Theoretical Investigation

摘要

This work is focused on the rectangular matrices obtained by unfolding multiway arrays. The rectangularity depends on how the unfolding procedure is realised. In this work we specify the multiway arrays being cubic. In other words, we focus on three way arrays and therefore get rectangular matrices whose column numbers is the square of their row numbers. The domain of these matrices is spanned by the Kronecker products of vectors whose number of elements match the row number of the considered matrix. We focus on the specific eigenvectors whose Kronecker products with a support vector is taken from the domain such that its image under the matrix is proportional to the eigenvector. We call these vectors first degree rectangular eigenvectors.