Hi.

Why is it a stochastic matrix always has the eigenvalue 1? I understand that the absolute value of a stochastic matrix can not exceed 1 since the determinant of the matrix has to be 1 or less than 1. But why will one eigenvalue always be 1?

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- February 24th 2010, 09:50 AMkrje1980Eigenvalue question
Hi.

Why is it a stochastic matrix always has the eigenvalue 1? I understand that the absolute value of a stochastic matrix can not exceed 1 since the determinant of the matrix has to be 1 or less than 1. But why will one eigenvalue always be 1? - February 24th 2010, 12:53 PMOpalg
- February 24th 2010, 11:34 PMkrje1980
Ah, that makes sense. Cheers! Thanks a lot!