Uncoupling the Perron Eigenvector Problem

  title={Uncoupling the Perron Eigenvector Problem},
  author={Carl D. Meyer},
For a nonnegative irreducible matrix A with spectral radius ρ , this paper is concerned with the determination of the unique normalized Perron vector π which satisfies A π = ρ π , π > 0 , ∑ j πj = 1 . It is explained how to uncouple a large matrix A into two or more smaller matrices — say P11,P22, · · · ,Pkk — such that this sequence of smaller matrices has the following properties. • Each Pii is also nonnegative and irreducible so that each Pii has a unique Perron vector π (i) . • Each Pii has… CONTINUE READING
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