If $A$ and $B$ are both column stochastic matrix with positive entries only, then $\|A\|_1=1, \|B\|_1=1$, could anyone tell me why $\|A-B\|_1\le 2$?
Thanks a lot.
2026-04-09 11:14:34.1775733274
one norm of column stochastic matrix
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By the triangle inequality, we have $\|A-B\|_1\le \|A\|_1 + \|B\|_1 = 1 + 1 = 2.$