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Extended Perron–Frobenius results
"... Matrices with entries that are smooth functions of a variable λ ∈ L and nonnegative when λ ∈ L − ⊂ L are considered. PerronFrobenius theory applies when the entries are nonnegative. Here, analogous results are shown to hold in neighbourhood of L−, with the various quantities varying smoothly. Th ..."
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Matrices with entries that are smooth functions of a variable λ ∈ L and nonnegative when λ ∈ L − ⊂ L are considered. PerronFrobenius theory applies when the entries are nonnegative. Here, analogous results are shown to hold in neighbourhood of L−, with the various quantities varying smoothly
PERRONFROBENIUS THEORY FOR COMPLEX MATRICES
"... Abstract. The purpose of this paper is to present a unified PerronFrobenius Theory for nonnegative, for real not necessarily nonnegative and for general complex matrices. The signreal spectral radius was introduced for general real matrices. This quantity was shown to share certain properties with ..."
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Cited by 3 (1 self)
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Abstract. The purpose of this paper is to present a unified PerronFrobenius Theory for nonnegative, for real not necessarily nonnegative and for general complex matrices. The signreal spectral radius was introduced for general real matrices. This quantity was shown to share certain properties
PerronFrobenius Properties of General Matrices
, 2007
"... A matrix is said to have the PerronFrobenius property if it has a positive dominant eigenvalue that corresponds to a nonnegative eigenvector. Matrices having this and similar properties are studied in this paper. Characterizations of collections of such matrices are given in terms of the spectral ..."
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Cited by 3 (1 self)
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A matrix is said to have the PerronFrobenius property if it has a positive dominant eigenvalue that corresponds to a nonnegative eigenvector. Matrices having this and similar properties are studied in this paper. Characterizations of collections of such matrices are given in terms of the spectral
The PerronFrobenius theorem for homogeneous monotone functions
 Transacton of AMS
, 2004
"... Abstract. If A is a nonnegative matrix whose associated directed graph is strongly connected, the PerronFrobenius theorem asserts that A has an eigenvector in the positive cone, (R+) n. We associate a directed graph to any homogeneous, monotone function, f:(R+) n → (R+) n, and show that if the grap ..."
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Cited by 41 (10 self)
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Abstract. If A is a nonnegative matrix whose associated directed graph is strongly connected, the PerronFrobenius theorem asserts that A has an eigenvector in the positive cone, (R+) n. We associate a directed graph to any homogeneous, monotone function, f:(R+) n → (R+) n, and show
Algorithms for Nonnegative Matrix Factorization
 In NIPS
, 2001
"... Nonnegative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minim ..."
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Cited by 1230 (5 self)
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Nonnegative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown
Applications of PerronFrobenius . . .
 J. MATH. BIOL. 44, 450–462 (2002)
, 2002
"... By the use of Perron–Frobenius theory, simple proofs are given of the Fundamental Theorem of Demography and of a theorem of Cushing and Yicang on the net reproductive rate occurring in matrix models of population dynamics. The latter result, which is closely related to the Stein–Rosenberg theorem ..."
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By the use of Perron–Frobenius theory, simple proofs are given of the Fundamental Theorem of Demography and of a theorem of Cushing and Yicang on the net reproductive rate occurring in matrix models of population dynamics. The latter result, which is closely related to the Stein–Rosenberg theorem
PerronFrobenius Theory over Real . . .
, 1995
"... Some of the main results of the PerronFrobenius theory of square nonnegative matrices over the reals are extended to matrices with elements in a real closed field. We use the results to prove the existence of a fractional power series expansion for the PerronFrobenius eigenvalue and normalized eig ..."
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Some of the main results of the PerronFrobenius theory of square nonnegative matrices over the reals are extended to matrices with elements in a real closed field. We use the results to prove the existence of a fractional power series expansion for the PerronFrobenius eigenvalue and normalized
Extension of the PerronFrobenius Theorem: From linear to homogeneous
, 2002
"... This paper deals with homogeneous cooperative systerns, a class of positive systems. It is shown that they admit a fairly simple asymptotic behavior, thereby generalizing the wellknown PerronFrobenius theorem from linear to homogeneous systems. As a corollary a simple criterion for global asympt ..."
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This paper deals with homogeneous cooperative systerns, a class of positive systems. It is shown that they admit a fairly simple asymptotic behavior, thereby generalizing the wellknown PerronFrobenius theorem from linear to homogeneous systems. As a corollary a simple criterion for global
ON GENERAL MATRICES HAVING THE PERRONFROBENIUS PROPERTY
, 2008
"... A matrix is said to have the PerronFrobenius propertyif its spectral radius is an eigenvalue with a corresponding nonnegative eigenvector. Matrices having this and similar properties are studied in this paper as generalizations of nonnegative matrices. Sets consisting of such generalized nonnegati ..."
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Cited by 14 (5 self)
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A matrix is said to have the PerronFrobenius propertyif its spectral radius is an eigenvalue with a corresponding nonnegative eigenvector. Matrices having this and similar properties are studied in this paper as generalizations of nonnegative matrices. Sets consisting of such generalized
Validated computation tool for the PerronFrobenius eigenvalues
"... A matrix with nonnegative entries has a special eigenvalue, the so called PerronFrobenius eigenvalue, which plays an important role in several fields of science [1]. In this paper we present a numerical tool to compute rigorous upper and lower bounds for the PerronFrobenius eigenvalue of nonne ..."
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A matrix with nonnegative entries has a special eigenvalue, the so called PerronFrobenius eigenvalue, which plays an important role in several fields of science [1]. In this paper we present a numerical tool to compute rigorous upper and lower bounds for the PerronFrobenius eigenvalue of nonnegative
Results 1  10
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28,047