论文标题
$ 4 \ times4 $嵌入式矩阵的开放式矩阵，其主要对数不是马尔可夫发电机
An open set of $4\times4$ embeddable matrices whose principal logarithm is not a Markov generator
论文作者
论文摘要
如果马尔可夫矩阵可以代表均匀的连续时间马尔可夫过程，则可以嵌入。众所周知，如果Markov矩阵具有真实和成对差异的特征值，则可以通过检查其主对数是否为速率矩阵来确定嵌入性。 Markov矩阵与身份矩阵的距离相同，或者该规则马尔可夫进程受到一定的限制。在本文中，我们证明该标准不能概括，我们提供了可嵌入的Markov矩阵集，并且其主体对数不是速率矩阵。
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.
