论文标题
马尔可夫矩阵和转换的一些结论
Some Conclusions on Markov Matrices and Transformations
论文作者
论文摘要
马尔可夫矩阵在随机过程的提交中具有重要作用。在本文中，我们将显示并证明对马尔可夫矩阵和转换的一系列结论，而不是注意随机过程，尽管这些结论对于研究随机过程很有用。我们得出的这些结论将使我们对马尔可夫矩阵和转换有了更深入的了解，请参阅特征值，特征向量和不变子空间的结构。同时，我们说明了结论的相应意义。对于任何马尔可夫矩阵和相应的转换，我们将空间分解为特征向量和不变子空间的直接总和。在此启发下，我们获得了两个关于马尔可夫矩阵和启发的变换的定理，我们得出结论，马尔可夫变换可能是一个有缺陷的矩阵 - 换句话说，可能是一个不可能的矩阵。具体来说，我们构建了一个不可吻合的马尔可夫矩阵来展示我们的思想列车。
Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although these conclusions are useful for studying stochastic processes. These conclusions we come to, which will make us have a deeper understanding of Markov matrices and transformations, refer to eigenvalues, eigenvectors and the structure of invariant subspaces. At the same time, we account for the corresponding significances of the conclusions. For any Markov matrix and the corresponding transformation, we decompose the space as a direct sum of an eigenvector and an invariant subspace. Enlightened by this, we achieve two theorems about Markov matrices and transformations inspired by which we conclude that Markov transformations may be a defective matrix--in other words, may be a nondiagonalizable one. Specifically, we construct a nondiagonalizable Markov matrix to exhibit our train of thought.
