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A note on the three-way generalization of the Jordan canonical form
- Source :
- Open Mathematics, Vol 16, Iss 1, Pp 897-912 (2018)
- Publication Year :
- 2018
- Publisher :
- De Gruyter, 2018.
-
Abstract
- The limit point 𝓧 of an approximating rank-R sequence of a tensor Ƶ can be obtained by fitting a decomposition (S, T, U) ⋅ 𝓖 to Ƶ . The decomposition of the limit point 𝓧 = (S, T, U) ⋅ 𝓖 with 𝓖 = blockdiag(𝓖1, … , 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 𝓖 j are zeros. In addition, we show how to turn 𝓖 j into canonical form under these conditions.
- Subjects :
- 15a18
Generalization
General Mathematics
010102 general mathematics
010103 numerical & computational mathematics
01 natural sciences
15a69
Algebra
low-rank tensor approximations
jordan canonical form
tensor decomposition
Three way
QA1-939
Tensor decomposition
Canonical form
0101 mathematics
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 23915455
- Volume :
- 16
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Open Mathematics
- Accession number :
- edsair.doi.dedup.....e62c19dd61a2a01760e37304533faac1