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Teaching Tip: When a Matrix and Its Inverse Are Stochastic

J. Ding and N. H. Rhee
The College Mathematics Journal
Vol. 44, No. 2 (March 2013), pp. 108-109
DOI: 10.4169/college.math.j.44.2.108
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Page Count: 2
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Summary A stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.

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