We know that :
- A matrix is regular if its determinant is non zero.
- A stochastic matrix is regular if at a certain power all elements are positive.
Question is how can I make the link between the two definitions, if there are any ? thanks in advance.
2026-03-30 11:53:26.1774871606
Regular matrix and regular stochastic matrix
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Consider this matrix \begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2} \end{bmatrix}The first power itself has all elements positive, it is doubly stochastic and still has a zero determinant.