Let T_{ijk} be a real 3rd order n x n x n tensor. Do there exist matrices U, V, W \in SO(n) such that the tensor S_{pqr} = sum_{i, j, k} U_{ip}V_{jq}W_{kr}T_{ijk} has the property:
1) S_{1qr} is diagonal;
2)S_{2qr} is upper-triangular?
I'm especially interested in case n=3.
Bhowmik Subrata
Can you send me the PDF or TeX file of the detail of the problem in my massage? I am interested to solve the problem.
0 votes
0 thanks
Evgeniy Martyushev
Dear Subrata, I would greatly appreciate it if you could solve the problem. I have no additional details, except that for n=3 numerical experiments show that the solution exists.
0 votes
0 thanks
- Badges
- Science topic
- Similar topics
- Geoscience
- Atmospheric Sciences
- Climate Science
- Climate Change
More Evgeniy Martyushev's questions See All
Similar questions and discussions