Symmetric matrix and their multiplications. (feature request)

[yuchihe]

For symmetric matrix, its storage and multiplication can be optimized.

For example, in BLAS, AA^T can be computed in syrk routine result in a upper traingle matrix representing the symmetric matrix.

However, there may be some work to be done to realized the following. for symmetric matrix T, C and T, computing TCT results in another symmetric matrix. It saves memory to store T and C as triangle matrix; it might be helpful to have a interface implying it means for symmetric matrix. And with the information of TCT is symmetric , It is helpful to have a function to just compute upper triangle elements in T and CT.

[Jutho]

I don't really understand what the specific question or feature request is?
Furthermore, since this is all about matrices, I don't really know if it belongs in TensorOperations.

Higher-rank tensors with permutation symmetry in the indices also allow reduced for storage, but the optimal representation, and how to implement operations such as tensor contractions in that case, is really a complicated and specialized topic, that is potentially also very dependent on specific hardware configuration.

[lkdvos]

I will close this for now as not planned. I think that since we don't have any concrete ideas for an implementation in the context of multi-dimensional arrays, and additionally the case you suggest would require operations involving 3 objects instead of pairwise operations, this might not be the right package for this right now.
Of course if there are any new ideas or concrete examples, feel free to re-open or file a new issue!