正特征值与双字母广义词
Positive eigenvalues and two-letter generalized words
摘要：
由两个字母$A$和$B$组成的广义词是$W=A^{α_1}B^{β_1}A^{α_2}B^{β_2}... A^{α_N}B^{β_N}$形式的表达式，其中指数$α_i$、$β_i$是非零实数。当用独立正定矩阵代替$A$和$B$时，我们感兴趣的是$W$是否一定有正的特征值.这是已知的情况下，当N=1，并已研究的情况下，所有的指数是积极的两个作者。然而，当指数符号混合时，情况就完全不同了（即使是2 × 2矩阵），这是本工作的重点。
英文摘要：
A generalized word in two letters $A$ and $B$ is an expression of the form $W=A^{α_1}B^{β_1}A^{α_2}B^{β_2}... A^{α_N}B^{β_N}$ in which the exponents $α_i$, $β_i$ are nonzero real numbers. When independent positive definite matrices are substituted for $A$ and $B$, we are interested in whether $W$ necessarily has positive eigenvalues. This is known to be the case when N=1 and has been studied in case all exponents are positive by two of the authors. When the exponent signs are mixed, however, the situation is quite different (even for 2-by-2 matrices), and this is the focus of the present work.
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。
