Monday, 24 December 2018

linear algebra - Largest eigenvalue of a symmetric "generalized doubly stochastic" matrix

Let ARn×n be a symmetric matrix whose rows and columns sum to one. A is not necessarily a doubly stochastic matrix, because negative entries are possible.



What can be said about the largest eigenvalue λ of A? Is there a "good" upper bound for λ?




Additional constraint: Suppose that |aij|1. Does λ1 hold?

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