Conjecture on the ML degree of rank-two 3 by n matrices

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Let V2\mathcal{V}_2 denote the variety of 3×n3 \times n matrices of rank at most 22, with n≥3n \geq 3. ML-degree conjecture. The ML degree of V2\mathcal{V}_2 equals

2n+1−6.2^{n+1}-6.

This conjecture concerns the number of complex critical points of the likelihood function for rank-constrained matrices. The supplied text gives no resolution status or further evidence beyond numerical experimentation.

References

Primary source

Jonathan Hauenstein, Jose Rodriguez and Bernd Sturmfels, “Maximum Likelihood for Matrices with Rank Constraints”, arXiv:1210.0198 (2013).

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