Let D+E be a stochastic matrix i. e., D+E be the matrix with each row sum 1, where D and E are non-zero nonnegetive, irreducible matrices, I-D being non-singular. Can it be proved that D+kE is diagonalizable for 0< |k| <1? I tried different pair of matrices (D, E), but each time it is diagonalizable, but I can't prove it generally. Please help me. Thanks in advance.
2026-02-23 04:46:00.1771821960
Diagonalizablity of a substochastic matrix
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