主对数不是Markov生成元的$4\times4$可嵌入矩阵的开集
An open set of $4\times4$ embeddable matrices whose principal logarithm is not a Markov generator
摘要：
一个马尔可夫矩阵是可嵌入的，如果它能表示一个齐次连续时间马尔可夫过程。众所周知，如果一个马尔可夫矩阵的特征值是实的且两两不同，那么可嵌入性可以通过检查其主对数是否是率矩阵来确定。这同样适用于足够接近单位矩阵的马尔可夫矩阵，或者规则一个受某些限制的马尔可夫过程。在本文中，我们证明了这一标准不能推广，我们提供了开放集的马尔可夫矩阵是可嵌入的，其主对数是一个不是一个率矩阵。
英文摘要：
A Markov matrix is embeddable if it can represent a homogeneous continuous-time Markov process. It is well known that if a Markov matrix has real and pairwise-different eigenvalues, then the embeddability can be determined by checking whether its principal logarithm is a rate matrix or not. The same holds for Markov matrices close enough to the identity matrix or that rule a Markov process subjected to certain restrictions. In this paper we prove that this criterion cannot be generalized and we provide open sets of Markov matrices that are embeddable and whose principal logarithm is a not a rate matrix.
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。
