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Let be a nonnegative matrix.
Let A ∈ R p × p be a nonnegative matrix.
Let (Ain M_{n}) be a nonnegative matrix.
Lemma 2.2 [7] Let A ∈ M n be a nonnegative matrix, and let ς(A) ≠ ∅.
Let (A = (a_{ij}) in M_{n}) be a nonnegative matrix.
Lemma 2.1 [6] Let A ∈ M n be a nonnegative matrix.
Similar(48)
Since is a nonnegative matrix with, we have that.
where is a positive diagonal matrix and is a nonnegative matrix function such that,.
Note that ({mathbf {H}}) is a nonnegative matrix; that is, all the elements of ({mathbf {H}}) are nonnegative.
Then, where and is a nonnegative matrix whose spectral radius if.
Proof It is clear that has diagonal entries ω1,..., ω t and is a nonnegative matrix by (2) and (4).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com