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Results tagged with tensor
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user 535019
4
votes
0
answers
123
views
Space of all orthogonal $2\times2\times2$ tensors
The solutions for order-$2$ tensors are clear so thus the simplest case is a $2\times2\times2$ tensor (with complex values). … This means if the $2\times2\times2$ tensor is denoted by $a_{i,j,k}$, then the following three equations must hold:
$$
\sum_{i=1}^2 \sum_{j=1}^2 a_{i,j,1} \overline{a_{i,j,2}} = 0
$$
$$\sum_{i=1}^2 \sum …
- 101
1
vote
0
answers
124
views
Space of all orthogonal partially complex $2\times2\times2$ tensors
I want to look at the simplest case first, namely a $2\times2\times2$ tensor. … This means if the $2\times2\times2$ tensor is denoted by $a_{i,j,k}$, then the following three equations must hold:
$$
\sum_{i=1}^2 \sum_{j=1}^2 a_{i,j,1} \overline{a}_{i,j,2} = 0
$$
$$\sum_{i=1}^2 \sum …
- 101