asisbanerjee Posted January 28, 2012 Share Posted January 28, 2012 I have to either prove or disprove with a counterexample the following staement: "Let A be an m by n row-stochastic matrix in which all entries are positive real numbers and let B be an n by m column-stochastic matrix with the same feature. Then all the eigen values of the m by m matrix AB are real." Can anyone help? Please note that AB is not necessarily symmetric (Hermitian). Link to comment Share on other sites More sharing options...
ajb Posted January 29, 2012 Share Posted January 29, 2012 Is this a variant of the Perron–Frobenius theorem? I do not know what row-stochastic matrix means. Link to comment Share on other sites More sharing options...
the tree Posted January 29, 2012 Share Posted January 29, 2012 I do not know what row-stochastic matrix means.A matrix where the entries in each row are real, positive and add up to 1. In other words, each row represents a discrete probability distribution. Link to comment Share on other sites More sharing options...
ajb Posted January 29, 2012 Share Posted January 29, 2012 A matrix where the entries in each row are real, positive and add up to 1. In other words, each row represents a discrete probability distribution. Cheers. Link to comment Share on other sites More sharing options...
Aethelwulf Posted June 12, 2012 Share Posted June 12, 2012 Cheers. yeah, I didn't know that either... was thinking more along the lines of row-echelon. Link to comment Share on other sites More sharing options...
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