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Journal articles on the topic 'Frobenius-Perron theorem'

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Published: 24 April 2022

Last updated: 30 July 2025

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1

Sine, Robert. "A nonlinear Perron-Frobenius theorem." Proceedings of the American Mathematical Society 109, no. 2 (1990): 331. http://dx.doi.org/10.1090/s0002-9939-1990-0948156-x.

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2

Evstigneev, Igor V., and Sergey A. Pirogov. "Stochastic nonlinear Perron–Frobenius theorem." Positivity 14, no. 1 (2009): 43–57. http://dx.doi.org/10.1007/s11117-008-0003-2.

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3

Stoyanov, Luchezar. "On the Ruelle–Perron–Frobenius theorem." Asymptotic Analysis 43, no. 1-2 (2005): 131–50. https://doi.org/10.3233/asy-2005-688.

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A comprehensive version of the Ruelle–Perron–Frobenius theorem is considered with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator.

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4

Dietzenbacher, Erik. "The non-linear Perron-Frobenius theorem." Journal of Mathematical Economics 23, no. 1 (1994): 21–31. http://dx.doi.org/10.1016/0304-4068(94)90033-7.

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5

Chang, K. C., K. Pearson, and T. Zhang. "Perron-Frobenius theorem for nonnegative tensors." Communications in Mathematical Sciences 6, no. 2 (2008): 507–20. http://dx.doi.org/10.4310/cms.2008.v6.n2.a12.

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6

Bidard, Christian, and Guido Erreygers. "Potron and the Perron–Frobenius Theorem." Economic Systems Research 19, no. 4 (2007): 439–52. http://dx.doi.org/10.1080/09535310701698563.

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7

NICOL, ROBERT. "Uma Extensão do Teorema de Perron-Frobenius." Brazilian Journal of Political Economy 10, no. 3 (1990): 384–96. http://dx.doi.org/10.1590/0101-31571990-0538.

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RESUMO Partindo de um teorema bastante simples de Scheffold, um conjunto de condições suficientes é encontrado para que o sistema pAp=Bp tenha uma solução com p>1 e p>0, onde A e B são nxn matrizes positivas. É mostrado que tal sistema seria uma extensão do sistema pAp=Ip para o qual o teorema de Perron-Frobenius é válido.

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8

Tateishi, Hiroshi. "Perron-Frobenius theorem for multi-valued mappings." Kodai Mathematical Journal 15, no. 2 (1992): 155–64. http://dx.doi.org/10.2996/kmj/1138039594.

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9

Kloeden, P. E., and A. M. Rubinov. "A generalization of the Perron–Frobenius theorem." Nonlinear Analysis: Theory, Methods & Applications 41, no. 1-2 (2000): 97–115. http://dx.doi.org/10.1016/s0362-546x(98)00267-3.

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10

Adachi, Toshiaki, and Toshikazu Sunada. "Twisted Perron-Frobenius theorem and L-functions." Journal of Functional Analysis 71, no. 1 (1987): 1–46. http://dx.doi.org/10.1016/0022-1236(87)90014-0.

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11

Gautier, Antoine, Francesco Tudisco, and Matthias Hein. "The Perron--Frobenius Theorem for Multihomogeneous Mappings." SIAM Journal on Matrix Analysis and Applications 40, no. 3 (2019): 1179–205. http://dx.doi.org/10.1137/18m1165037.

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12

Ding, Jiu, and Temple H. Fay. "The Perron-Frobenius Theorem and Limits in Geometry." American Mathematical Monthly 112, no. 2 (2005): 171. http://dx.doi.org/10.2307/30037416.

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13

Thiemann, René. "A Perron–Frobenius theorem for deciding matrix growth." Journal of Logical and Algebraic Methods in Programming 123 (November 2021): 100699. http://dx.doi.org/10.1016/j.jlamp.2021.100699.

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14

Ding, Jiu, and Temple H. Fay. "The Perron-Frobenius Theorem and Limits in Geometry." American Mathematical Monthly 112, no. 2 (2005): 171–75. http://dx.doi.org/10.1080/00029890.2005.11920182.

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15

Bapat, R. B. "A max version of the Perron-Frobenius theorem." Linear Algebra and its Applications 275-276 (May 1998): 3–18. http://dx.doi.org/10.1016/s0024-3795(97)10057-x.

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16

Gaubert, Stéphane, and Jeremy Gunawardena. "The Perron-Frobenius theorem for homogeneous, monotone functions." Transactions of the American Mathematical Society 356, no. 12 (2004): 4931–50. http://dx.doi.org/10.1090/s0002-9947-04-03470-1.

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17

Fan, Aihua, and Yunping Jiang. "On Ruelle-Perron-Frobenius Operators.¶I. Ruelle Theorem." Communications in Mathematical Physics 223, no. 1 (2001): 125–41. http://dx.doi.org/10.1007/s002200100538.

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18

Eschenbach, Carolyn A., and Charles R. Johnson. "A combinatorial converse to the Perron-Frobenius theorem." Linear Algebra and its Applications 136 (July 1990): 173–80. http://dx.doi.org/10.1016/0024-3795(90)90026-9.

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19

Pillai, S. U., T. Suel, and Seunghun Cha. "The Perron-Frobenius theorem: some of its applications." IEEE Signal Processing Magazine 22, no. 2 (2005): 62–75. http://dx.doi.org/10.1109/msp.2005.1406483.

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20

Bidard, C., and M. Zerner. "The Perron-Frobenius theorem in relative spectral theory." Mathematische Annalen 289, no. 1 (1991): 451–64. http://dx.doi.org/10.1007/bf01446582.

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21

Babaei, E., I. V. Evstigneev, and S. A. Pirogov. "Stochastic fixed points and nonlinear Perron–Frobenius theorem." Proceedings of the American Mathematical Society 146, no. 10 (2018): 4315–30. http://dx.doi.org/10.1090/proc/14075.

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22

Fehlmann, Thomas, and Eberhard Kranich. "The World Formula and the Theorem of Perron-Frobenius: How to Solve (Almost All) Problems of the World." Athens Journal of Sciences 10, no. 2 (2023): 95–110. http://dx.doi.org/10.30958/ajs.10-2-3.

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Transfer Functions relate the output or response of a system such as a filter circuit to the input or stimulus . The response can be measured; the is the unknown. Solving the World Formula not only explains how analog images and voice can be digitally stored, but also many methods and techniques such as Big Data and Artificial Intelligence. For linear functions between vector spaces, the Eigenvector Method makes calculating a solution easy, if it exists. Numerical algorithms are available for solving. Thus, the method is suitable for teaching students who are interested in the foundations of s

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23

Anh, Bui The, and D. D. X. Thanh. "A Perron-Frobenius Theorem for Positive Quasipolynomial Matrices Associated with Homogeneous Difference Equations." Journal of Applied Mathematics 2007 (2007): 1–6. http://dx.doi.org/10.1155/2007/26075.

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We extend the classical Perron-Frobenius theorem for positive quasipolynomial matrices associated with homogeneous difference equations. Finally, the result obtained is applied to derive necessary and sufficient conditions for the stability of positive system.

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24

Boyle, Phelim, and Thierno N'Diaye. "Correlation Matrices with the Perron Frobenius Property." Electronic Journal of Linear Algebra 34 (February 21, 2018): 240–68. http://dx.doi.org/10.13001/1081-3810.3616.

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This paper investigates conditions under which correlation matrices have a strictly positive dominant eigenvector. The sufficient conditions, from the Perron-Frobenius theorem, are that all the matrix entries are positive. The conditions for a correlation matrix with some negative entries to have a strictly positive dominant eigenvector are examined. The special structure of correlation matrices permits obtaining of detailed analytical results for low dimensional matrices. Some specific results for the $n$-by-$n$ case are also derived. This problem was motivated by an application in portfolio

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25

STADLBAUER, MANUEL. "ON RANDOM TOPOLOGICAL MARKOV CHAINS WITH BIG IMAGES AND PREIMAGES." Stochastics and Dynamics 10, no. 01 (2010): 77–95. http://dx.doi.org/10.1142/s0219493710002863.

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We introduce a relative notion of the "big images and preimages"-property for random topological Markov chains. This condition then implies that a relative version of the Ruelle–Perron–Frobenius theorem holds with respect to summable and locally Hölder continuous potentials.

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26

Dealba, Luz Maria. "Cubic polynomials, their roots and the Perron-Frobenius theorem." International Journal of Mathematical Education in Science and Technology 33, no. 1 (2002): 96–111. http://dx.doi.org/10.1080/00207390210212.

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27

Yang, Yuning, and Qingzhi Yang. "Further Results for Perron–Frobenius Theorem for Nonnegative Tensors." SIAM Journal on Matrix Analysis and Applications 31, no. 5 (2010): 2517–30. http://dx.doi.org/10.1137/090778766.

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28

Aeyels, Dirk, and Patrick De Leenheer. "Extension of the Perron--Frobenius Theorem to Homogeneous Systems." SIAM Journal on Control and Optimization 41, no. 2 (2002): 563–82. http://dx.doi.org/10.1137/s0363012900361178.

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29

Tarazaga, Pablo, Marcos Raydan, and Ana Hurman. "Perron–Frobenius theorem for matrices with some negative entries." Linear Algebra and its Applications 328, no. 1-3 (2001): 57–68. http://dx.doi.org/10.1016/s0024-3795(00)00327-x.

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30

Friedland, S., S. Gaubert, and L. Han. "Perron–Frobenius theorem for nonnegative multilinear forms and extensions." Linear Algebra and its Applications 438, no. 2 (2013): 738–49. http://dx.doi.org/10.1016/j.laa.2011.02.042.

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31

Lagro, Matthew, Wei-Shih Yang, and Sheng Xiong. "A Perron–Frobenius Type of Theorem for Quantum Operations." Journal of Statistical Physics 169, no. 1 (2017): 38–62. http://dx.doi.org/10.1007/s10955-017-1862-3.

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32

Rath, Kali. "On non-linear extensions of the Perron-Frobenius theorem." Journal of Mathematical Economics 15, no. 1 (1986): 59–62. http://dx.doi.org/10.1016/0304-4068(86)90023-6.

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33

Livshits, L., G. MacDonald, and H. Radjavi. "A Perron-Frobenius-type Theorem for Positive Matrix Semigroups." Positivity 21, no. 1 (2016): 61–72. http://dx.doi.org/10.1007/s11117-016-0403-7.

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34

Bush, Brandon, Jordan Culp, and Kelly Pearson. "Perron–Frobenius theorem for hypermatrices in the max algebra." Discrete Mathematics 342, no. 1 (2019): 64–73. http://dx.doi.org/10.1016/j.disc.2018.09.023.

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35

Nussbaum, R. D., and S. M. Verduyn Lunel. "Generalizations of the Perron-Frobenius theorem for nonlinear maps." Memoirs of the American Mathematical Society 138, no. 659 (1999): 0. http://dx.doi.org/10.1090/memo/0659.

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36

Chang, K. C. "Nonlinear extensions of the Perron–Frobenius theorem and the Krein–Rutman theorem." Journal of Fixed Point Theory and Applications 15, no. 2 (2014): 433–57. http://dx.doi.org/10.1007/s11784-014-0191-2.

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37

Siems, Tobias. "Markov Chain Monte Carlo on finite state spaces." Mathematical Gazette 104, no. 560 (2020): 281–87. http://dx.doi.org/10.1017/mag.2020.51.

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We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we prove a pivotal convergence theorem for finite Markov chains and a minimal version of the Perron-Frobenius theorem. Subsequently, we briefly discuss two fundamental MCMC methods, the Gibbs and Metropolis-Hastings sampler. Only very basic knowledge about matrices, convergence of real sequences and probability theory is required.

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38

DANERS, DANIEL, and JOCHEN GLÜCK. "THE ROLE OF DOMINATION AND SMOOTHING CONDITIONS IN THE THEORY OF EVENTUALLY POSITIVE SEMIGROUPS." Bulletin of the Australian Mathematical Society 96, no. 2 (2017): 286–98. http://dx.doi.org/10.1017/s0004972717000260.

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We carry out an in-depth study of some domination and smoothing properties of linear operators and of their role within the theory of eventually positive operator semigroups. On the one hand, we prove that, on many important function spaces, they imply compactness properties. On the other hand, we show that these conditions can be omitted in a number of Perron–Frobenius type spectral theorems. We furthermore prove a Kreĭn–Rutman type theorem on the existence of positive eigenvectors and eigenfunctionals under certain eventual positivity conditions.

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39

Li, Wenxi, and Zhongzhi Wang. "A NOTE ON RÉNYI'S ENTROPY RATE FOR TIME-INHOMOGENEOUS MARKOV CHAINS." Probability in the Engineering and Informational Sciences 33, no. 4 (2018): 579–90. http://dx.doi.org/10.1017/s026996481800044x.

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AbstractIn this note, we use the Perron–Frobenius theorem to obtain the Rényi's entropy rate for a time-inhomogeneous Markov chain whose transition matrices converge to a primitive matrix. As direct corollaries, we also obtain the Rényi's entropy rate for asymptotic circular Markov chain and the Rényi's divergence rate between two time-inhomogeneous Markov chains.

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40

Afshin, Hamid Reza, and Ali Reza Shojaeifard. "A max version of Perron--Frobenius theorem for nonnegative tensor." Annals of Functional Analysis 6, no. 3 (2015): 145–54. http://dx.doi.org/10.15352/afa/06-3-12.

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41

Horiguchi, T., and Y. Fukui. "An Extension of Perron-Frobenius Theorem for Positive Symmetric Matrices." Progress of Theoretical Physics 88, no. 6 (1992): 1219–23. http://dx.doi.org/10.1143/ptp/88.6.1219.

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42

Yang, Qingzhi, and Yuning Yang. "Further Results for Perron–Frobenius Theorem for Nonnegative Tensors II." SIAM Journal on Matrix Analysis and Applications 32, no. 4 (2011): 1236–50. http://dx.doi.org/10.1137/100813671.

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43

Keener, James P. "The Perron–Frobenius Theorem and the Ranking of Football Teams." SIAM Review 35, no. 1 (1993): 80–93. http://dx.doi.org/10.1137/1035004.

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44

Cheng, Yun, Timothy Carson, and Mohamed B. M. Elgindi. "A Note on the Proof of the Perron-Frobenius Theorem." Applied Mathematics 03, no. 11 (2012): 1697–701. http://dx.doi.org/10.4236/am.2012.311235.

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45

McNamara, John M. "Optimal life histories: A generalisation of the Perron-Frobenius theorem." Theoretical Population Biology 40, no. 2 (1991): 230–45. http://dx.doi.org/10.1016/0040-5809(91)90054-j.

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46

Hawkins, Thomas. "Continued fractions and the origins of the Perron–Frobenius theorem." Archive for History of Exact Sciences 62, no. 6 (2008): 655–717. http://dx.doi.org/10.1007/s00407-008-0026-x.

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47

Stoyanov, Luchezar. "On Gibbs Measures and Spectra of Ruelle Transfer Operators." Canadian Mathematical Bulletin 60, no. 2 (2017): 411–21. http://dx.doi.org/10.4153/cmb-2016-073-2.

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AbstractWe prove a comprehensive version of the Ruelle–Perron–Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is that the Hölder constant of the function generating the operator appears only polynomially, not exponentially as in previously known estimates.

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48

Delgado, Jorge, Héctor Orera, and J. M. Peña. "Accurate Computations with Block Checkerboard Pattern Matrices." Mathematics 12, no. 6 (2024): 853. http://dx.doi.org/10.3390/math12060853.

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In this work, block checkerboard sign pattern matrices are introduced and analyzed. They satisfy the generalized Perron–Frobenius theorem. We study the case related to total positive matrices in order to guarantee bidiagonal decompositions and some linear algebra computations with high relative accuracy. A result on intervals of checkerboard matrices is included. Some numerical examples illustrate the theoretical results.

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49

Li, Pei-Sen, and Pan Zhao. "The Subdominant Eigenvalue of Möbius Monotone Transition Probability Matrix." Axioms 14, no. 7 (2025): 493. https://doi.org/10.3390/axioms14070493.

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We establish a Perron–Frobenius-type theorem for the subdominant eigenvalue of Möbius monotone transition matrices defined on partially ordered state spaces. This result extends the classical work of Keilson and Kester, where they considered stochastically monotone transition matrices in a totally ordered setting. Furthermore, we show that this subdominant eigenvalue is the geometric ergodicity rate.

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50

Trow, Paul. "Resolving maps which commute with a power of the shift." Ergodic Theory and Dynamical Systems 6, no. 2 (1986): 281–93. http://dx.doi.org/10.1017/s014338570000345x.

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AbstractIn this paper, we prove an extension of a theorem of Marcus, which says that every subshift of finite type of entropy log n, n an integer, factors onto the full n-shift. Let p(x) be a monic polynomial, irreducible over ℚ, whose coefficients (except for the leading coefficient) are non-positive integers. Suppose C(λ) is the companion matrix of p(x), where λ is the largest real root of p(x) (λ exists, by the Perron-Frobenius theorem). Then for any aperiodic, non-negative, integral matrix A, with Perron value λ, we give necessary and sufficient conditions for the existence of a positive i

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