Abstract:
Two new inclusion regions of eigenvalue different from 1 of stochastic matrices are given by using the
![](https://image.hanspub.org/IMAGE/Edit_e55a719a-13b0-4fcb-a05f-18917aec326c.png)
-eigenvalue inclusion theorem and the theory of modified matrices; and two new sufficient conditions of stochastic matrices nonsingular are obtained. Numerical examples are given to show that the existing results are improved in some cases.