本論文證明了廣義隨機矩陣所有的核心主要自反矩陣的聯集具有稠密性。然後再找一些介 於廣義隨機矩陣和其核心主要自反矩陣之間的那些矩陣的特性。最後，在這些中間矩陣當中找 到一個特殊的矩陣子群。

In this paper, we prove that the union of the cores of all primitive idempotent of real stochastic matrices is dense. After that we get a characterization of the matrices between the real stochastic matrices and the union of the cores of all primitive idempotent of real stochastic matrices. Finally we get a special linear subgroup.