Tensor-Tensor Products, Group Representations, and Semidefinite Programming
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Abstract (arXiv)
The starM-family of tensor-tensor products is a framework which generalizes many properties from linear algebra to third order tensors. Here, we investigate positive semidefiniteness and semidefinite programming under the starM-product. Critical to our investigation is a connection between the choice of matrix M in the starM-product and the representation theory of an underlying group action. Using this framework, third order tensors equipped with the starM-product are a natural setting for the study of invariant semidefinite programs. As applications of the M-SDP framework, we provide a characterization of certain nonnegative quadratic forms and solve low-rank tensor completion problems.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 11 of its 40 references that are in the map. First posted on arXiv 17 Jul 2025.
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11 of 40 references.
References · 11
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- 2020Symmetry Adapted Gram Spectrahedracited by 1
- 2022Group-invariant tensor train networks for supervised learningcited by 1
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Citing papers per year: 2026: 1.
1 paper.