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Mathematics, 22.04.2020 03:27 arteria3
Stochastic n-by-n matrices Recall that an n × n matrix A is said to be stochastic if the following conditions are satisfied (a) Entries of A are non negative, that is ai, j ≥ 0 for all 1 ≤ i ≤ n and all 1 ≤ j ≤ n. (b) Each column of A sums to 1, that is Pn i=1 ai, j = 1, for all 1 ≤ j ≤ n. Let S and M be arbitrary stochastic n-by-n matrices. (a) Show that λ = 1 is an eigenvalue of S. 2 points (b) Show that S 2 is also a stochastic matrix. 2 points (c) Does MS have to be stochastic? Explain
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Stochastic n-by-n matrices Recall that an n × n matrix A is said to be stochastic if the following c...
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