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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > SHIRI SIVAN:
All reports by Author Shiri Sivan:

TR26-073 | 11th May 2026
Vishwas Bhargava, Leonard Schulman, Shiri Sivan

An Algorithmic Proof of Kruskal’s Tensor Decomposition Theorem

A famous theorem of Kruskal gives the simplest and arguably most fundamental criterion under which a tensor is guaranteed a unique minimum-rank decomposition. Kruskal's condition requires that the sum of the Kruskal ranks $\{k_i\}_{i=1}^m$ of the components satisfies $\sum_{i \in [m]} k_i \ge 2r + m - 1$, where $r$ ... more >>>




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