Perron Vectors of an Irreducible Nonnegative Interval Matrix
نویسنده
چکیده
As is well known, an irreducible nonnegative matrix possesses a uniquely determined Perron vector. As the main result of this paper we give a description of the set of Perron vectors of all the matrices contained in an irreducible nonnegative interval matrix A. This result is then applied to show that there exists a subset A∗ of A parameterized by n parameters (instead of n2 ones in the description of A) such that for each A ∈ A there exists a matrix A′ ∈ A∗ having the same spectral radius and the same Perron vector as A.
منابع مشابه
Some results on the block numerical range
The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.
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