mlsanityData to 7 Oct 2026

Positive semidefinite rank

arXiv 1407.4095 ↗First posted 15 Jul 2014math.OC cs.DM math.COcited by 10

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Abstract (arXiv)

Let M be a p-by-q matrix with nonnegative entries. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices Ai, Bj of size k × k such that Mij = trace(Ai Bj). The psd rank has many appealing geometric interpretations, including semidefinite representations of polyhedra and information-theoretic applications. In this paper we develop and survey the main mathematical properties of psd rank, including its geometry, relationships with other rank notions, and computational and algorithmic aspects.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Jul 2014.

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Citing papers per year: 2021: 3; 2022: 0; 2023: 0; 2024: 3; 2025: 1; 2026: 3.

10 papers.

  1. 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?cited by 22
  2. 2024Sum of Squares Circuitscited by 21
  3. 2024On the Relationship Between Monotone and Squared Probabilistic Circuitscited by 14
  4. 2025Alternating Direction Method of Multipliers for Nonlinear Matrix Decompositionscited by 3
  5. 2021A Non-commutative Extension of Lee-Seung's Algorithm for Positive Semidefinite Factorizationscited by 2
  6. 2026Manifold-based Algorithms for the Hadamard Decompositioncited by 2
  7. 2021Restricted Hidden Cardinality Constraints in Causal Modelscited by 1
  8. 2021Multiplicative updates for symmetric-cone factorizationscited by 0
  9. 2026On the Complexity of Low-Rank Matrix Signing and Entrywise Power Matrix Factorizationcited by 0
  10. 2026Quantum Coordination Advantages in AI State-Tracking Tasks: Semantic Compilation and Latent Memorycited by 0