A note on the three-way generalization of the Jordan canonical form

作者：Cui, Lu-Bin^*; Li, Ming-Hui

来源：Open Mathematics, 2018, 16(1): 897-912.

DOI：10.1515/math-2018-0078

• Low-rank tensor approximations
• Jordan canonical form
• Tensor decomposition

The limit point X of an approximating rank-R sequence of a tensor Z can be obtained by fitting a decomposition (S, T, U) . G to Z. The decomposition of the limit point X = (S, T, U) . G with G = blockdiag (G(1),...,G(m)) can be seen as a three order generalization of the real Jordan canonical form. The main aim of this paper is to study under what conditions we can turn G(j) into canonical form if some of the upper triangular entries of the last three slices of (Gj) are zeros. In addition, we show how to turn G(j) into canonical form under these conditions.

• 出版日期2018-8-8
• 单位河南师范大学