Penrose notation for tensor "list"

Hello all,
Is there any extension of the Tensor Diagrammatic notation for expressing “list“ indices of tensors?
By list, I mean any sequence of tensors of the same tensor space that could, in principle, be seen as a tensor of order +1.
The point is that these indices would not respect the Einstein convention; they are not summed over and can be repeated any number of times.

In computer science, this is handled by checking indices on both sides of the equation, differently from the Penrose notation, where we would like to infer the shape of the contraction result.

Here is a simple example of what I would like to have, with “T“ legs for these list indexes:

Any thoughts on this would be appreciated!
Cheers,
Marco

Hello MarcoTT,

I usually use a super-diagonal tensor for this case.

If my understanding is correct, your example can be represented as follow:


This type of multiplication is the same structure of Hadamard (elementwise) product or Khatri-Rao product.
If you are interested, please refer the following tutorial preprint.
[2411.16094] Very Basics of Tensors with Graphical Notations: Unfolding, Calculations, and Decompositions

Best regards,

Yokota

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