The Collins–Dykema–Torres-Ayala positivity conjecture for symmetric matrices

From papers

Let AA and BB be symmetric matrices of the same size. For integers mm and rr with mrm\geq r and both mm and rr even, consider the coefficient of trt^r in

trace((A+tB)m).\mathsf{trace}((A+tB)^m).

Collins–Dykema–Torres-Ayala conjecture. This coefficient is non-negative.

This question is a symmetric-matrix variant of the BMV positivity question. It was proved by Stahl and later simplified by Eremenko, so the conjecture is solved.

Progress summary

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Sources & referencesView supporting material

Primary source

Nathaniel K. Green and Edward D. Kim, “Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala”, arXiv:2307.06311 (2023).

Additional references

2 papers in this index state this conjecture (2021–2023). The statement above is taken from the most recent of them; the others are arXiv:2110.12528.

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