两个Hermite正定矩阵广义字的正特征值
Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices
摘要：
定义两个正定（复厄米特）矩阵$A$和$B$中的一个字为$A$和$B$的实幂的有限乘积。哪些词只有正特征值的问题得到解决。这个问题提出了一段时间前在理论物理学的一个长期存在的问题，它是以前接近的作者为词在两个真正的正定矩阵与积极的整指数。一大类的话，保证积极的特征值确定，并提供了相当多的证据的猜想，没有其他的话。
英文摘要：
We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a long-standing problem in theoretical physics, and it was previously approached by the authors for words in two real positive definite matrices with positive integral exponents. A large class of words that do guarantee positive eigenvalues is identified, and considerable evidence is given for the conjecture that no other words do.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
