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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
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
Generalized Perron–Frobenius Theorem for Nonsquare Matrices
, 2014
"... The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of sci ..."
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The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields
Generalizations of the PerronFrobenius Theorem for Nonlinear Maps
, 1999
"... . Let K n = fx 2 R n j x i 0; 1 i ng and suppose that f : K n ! K n is nonexpansive with respect to the l 1 norm, kxk 1 = P n i=1 x i , and f(0) = 0. It is known (see [1]) that for every x 2 K n there exists a periodic point = x 2 K n (so f p () = for some minimal positive integ ..."
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Cited by 2 (0 self)
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set Q(n) determined by certain arithmetical and combinatorial constraints. In a sequel to this paper [14] it is proved that P 2 (n) = Q(n) for all n, but the computation of Q(n) is highly nontrivial. Here we derive a variety of theorems about admissible arrays and use these theorems to compute Q
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 spectrum for random maps and its approximation
, 2001
"... To study the convergence to equilibrium in random maps we developed the spectral theory of the corresponding transfer (PerronFrobenius) operators acting in a certain Banach space of generalized functions. The random maps under study in a sense ll the gap between expanding and hyperbolic systems si ..."
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Cited by 5 (2 self)
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To study the convergence to equilibrium in random maps we developed the spectral theory of the corresponding transfer (PerronFrobenius) operators acting in a certain Banach space of generalized functions. The random maps under study in a sense ll the gap between expanding and hyperbolic systems
GENERALISATION OF THE PERRONFROBENIUS THEORY TO MATRIX PENCILS ∗
"... Dedicated to Hans Schneider on the occasion of his 80th birthday Abstract. We present a new extension of the wellknown PerronFrobenius theorem to regular matrix pairs (E, A). The new extension is based on projector chains and is motivated from the solution of positive differentialalgebraic system ..."
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Cited by 4 (0 self)
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Dedicated to Hans Schneider on the occasion of his 80th birthday Abstract. We present a new extension of the wellknown PerronFrobenius theorem to regular matrix pairs (E, A). The new extension is based on projector chains and is motivated from the solution of positive differential
Results 1  10
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313,057