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For a stochastic matrix $P$ of size $n$, we define
$$\|P\|_1 := \max_{j \in [n]} \sum_{i \in [n]}|P(i,j)|$$
i.e., the maximum column sum, which is based on the $\|\cdot\|_1$ matrix norm. Now, although $\|P\|_\infty$ for all stochastic matrices (defined as the maximum row sum) is equal to one by...