Sums of Hermitian squares as an approach to the BMV conjecture
Sums of Hermitian squares as an approach to the BMV conjecture
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Hermitian 平方和作为 BMV 猜想的一种方法
DOI：
10.1080/03081080903119137
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发表时间：
2008
影响因子：
1.1
通讯作者：
Sabine Burgdorf
中科院分区：
文献类型：
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作者：
Sabine Burgdorf
Lieb和Seiringer在他们对Bessis-Moussa-Villani猜想的重新表述中指出，当A和B是任何两个大小相同的半正定矩阵时，多项式p（t）= tr（（A +tr B）m）的所有系数都是非负的。我们将证明，对于所有的m∈ n，p（t）中t4的系数是非负的，使用连接到非交换多项式的厄米特平方和，这已经建立了Klep和Schweighthorn。这意味着希拉尔的一个著名的结果是，当0 ≤ k ≤ 4时，t k的系数是非负的，当m ≥ k ≥ m − 4时，t k的系数也是非负的。
Lieb and Seiringer stated in their reformulation of the Bessis–Moussa–Villani conjecture that all coefficients of the polynomial p(t) = tr((A +tr B) m ) are non-negative whenever A and B are any two positive semidefinite matrices of the same size. We will show that for all m∈ℕ the coefficient of t 4 in p(t) is non-negative, using a connection to sums of Hermitian squares of non-commutative polynomials which has been established by Klep and Schweighofer. This implies by a well-known result of Hillar that the coefficients of t k are non-negative for 0 ≤ k ≤ 4, and by symmetry as well for m ≥ k ≥ m − 4.
Hermitian 平方和与 BMV 猜想
影响因子：
1.6
作者：
I. Klep;M. Schweighofer
通讯作者：
M. Schweighofer