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Topic: Frobenius theorem

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Frobenius method

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Georg Frobenius

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	Frobenius theorem - Wikipedia, the free encyclopedia
		Ferdinand Georg Frobenius has several theorems with his name in them, more than one of which have only his name.
		Frobenius theorem in differential geometry and topology for integrable subbundles;
		Frobenius reciprocity theorem in group representation theory describing the reciprocity relation between restricted and induced representations on a subgroup;
	en.wikipedia.org /wiki/Frobenius_theorem (146 words)

	Perron–Frobenius theorem - Wikipedia, the free encyclopedia
		In mathematics, the Perron–Frobenius theorem, named after Oskar Perron and Ferdinand Georg Frobenius, is a theorem in matrix theory about the eigenvalues and eigenvectors of a real positive n×n matrix:
		This result has a natural interpretation in the theory of finite Markov chains (where it is the matrix-theoretic equivalent of the convergence of a finite Markov chain, formulated in terms of the transition matrix of the chain; see, for example, the article on the subshift of finite type).
		The Perron–Frobenius theorem can be further generalized to the class of block-indecomposable non-negative matrices (called "irreducible" in reference [1] below, also called regular in the stochastic case).
	en.wikipedia.org /wiki/Frobenius-Perron_equation (544 words)

	[No title]
		When Q is unramified: G_Q isomorphic to Gal_k l; definition of the Frobenius symbol of Q in L:K. Concrete characterization of the Frobenius symbol.
		Relating Cebotarev's density theorem for the 13th cyclotomic field to the distribution of primes mod 13.
		Typical application (already proved by Frobenius): density of primes with a given factorization type in L is the density of permutations with that cycle type in the Galois closure of L. What the existence theorem says.
	cr.yp.to /2000-515/inclass.html (3147 words)

	Some Useful Theorems
		Theorem: (Fundamental Theorem of Algebra) an algebraic expression of the polynomial form:
		Proofs of the various aspects of the Perron-Frobenius theorems (plus extensions) are given in Debreu and Herstein (1953), Morishima (1964), Murata (1977), Nikaido (1960), Pasinetti (1975), Takayama (1974) and Kurz and Salvadori (1995).
		Theorem: (Routh-Hurwitz) A necessary and sufficient condition that all the roots of the n-degree polynomial equation with real coefficients:
	cepa.newschool.edu /het/essays/math/useful.htm (546 words)

	THE PERRON-FROBENIUS THEOREM
		Complex eigenvalues are a real possibility as only symmetric matrices are guaranteed to not have them, and very few of the matrices we have been discussing, in application, will be symmetric with the notable exception of undirected graphs.
		In general, it should be remarked that graph theory and nonnegative matrices have a very strong relationship and that the Perron-Frobenius Theorem is often a powerful tool in graph theory.
		The Perron-Frobenius Theorem has proven to be a consistently powerful result for examining certain nonnegative matrices arising in discrete models.
	www.prenhall.com /divisions/esm/app/ph-linear/leon/html/perron.html (2166 words)

	Burnside's Theorem
		In the proof of Burnside's Theorem in the book (Theorem 4.3), I use Frobenius' Theorem (which, as remarked on Page 36, uses character theory).
		Professor Ram Abhyankar pointed out to me that this theorem occurs already in the first edition of Burnside's book (and hence must have a proof not using character theory!) Here is the proof.
		By Theorem 4.4, if a primitive group has more than one minimal normal subgroup, then it has just two, and each is the centraliser of the other, so they are non-abelian and regular.
	www.maths.qmw.ac.uk /~pjc/permgps/burnside.html (241 words)

	Generalizations Of The Perron-Frobenius Theorem For Nonlinear Maps - Nussbaum, Lunel (ResearchIndex) (Site not responding. Last check: 2007-10-31)
		A SPECTRAL THEOREM FOR CONVEX MONOTONE HOMOGENEOUS MAPS..
		Generalizations of the Perron-Frobenius theorem for nonlinear maps.
		9 A nonlinear Perron-Frobenius theorem (context) - Sine - 1990
	citeseer.ist.psu.edu /348724.html (608 words)

	Citebase - The single-leaf Frobenius Theorem with Applications (Site not responding. Last check: 2007-10-31)
		Authors: Piccione, Paolo; Tausk, Daniel V. Using the notion of Levi form of a smooth distribution, we discuss the local and the global problem of existence of one horizontal section of a smooth vector bundle endowed with a horizontal distribution.
		The analysis will lead to the formulation of a "one-leaf" analogue of the classical Frobenius integrability theorem in elementary differential geometry.
		Second, we will prove a general version of the classical Cartan-Ambrose-Hicks Theorem giving conditions on the existence of an affine map with prescribed differential at one point between manifolds endowed with connections.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0510555 (179 words)

	Springer Online Reference Works
		» Encyclopaedia of Mathematics »; P » Perron–Frobenius theorem
		Frobenius [2] gave the full form of the theorem.
		G. Frobenius, "Ueber Matrizen aus nicht negativen Elementen" Sitzungsber.
	eom.springer.de /P/p072350.htm (140 words)

	A characterization of spectral abscissa and Perron-Frobenius theorem of positive linear functional differential ...
		A characterization of spectral abscissa and Perron-Frobenius theorem of positive linear functional differential equations -- Ngoc and Lee 23 (3): 259 -- IMA Journal of Mathematical Control and Information
		A characterization of spectral abscissa and Perron–Frobenius theorem of positive linear functional differential equations
		Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues.
	imamci.oxfordjournals.org /cgi/content/short/23/3/259?rss=1 (232 words)

	Atlas: Twisted Burnside-Frobenius theorem for discrete groups by Alexander Fel'shtyn (Site not responding. Last check: 2007-10-31)
		It is proved for a wide class of groups including polycyclic and finitely generated polynomial growth groups that the Reidemeister number of an automorphism is equal to the number of finite-dimensional fixed points of induced map on the unitary dual space, if one of these numbers is finite.
		This theorem is a natural generalisation to infinite discrete groups of the classical Burnside-Frobenius theorem.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqu-57.
	atlas-conferences.com /cgi-bin/abstract/caqu-57 (148 words)

	Amazon.com: Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps (Memoirs of the American Mathematical ... (Site not responding. Last check: 2007-10-31)
		Amazon.com: Generalizations of the Perron-Frobenius Theorem for Nonlinear Maps (Memoirs of the American Mathematical Society): Books: Roger D. Nussbaum,S. Verduyn Lunel
		The classical Frobenius-Perron Theorem establishes the existence of periodic points of certain linear maps in ${\mathbb R}^n$.
		The authors present generalizations of this theorem to nonlinear maps.
	www.amazon.com /exec/obidos/tg/detail/-/0821809695?v=glance (420 words)

	Links to the Perron-Frobenius theorem (Site not responding. Last check: 2007-10-31)
		The Perron-Frobenius theorem says that if A is a positive stochastic matrix (that is, the entries of A are positive and the columns of A sum to 1) then
		Here are some links to proofs and further discussion of the Perron-Frobenius theorem.
		Several proofs, discussion, examples of use in applied math.
	www.csudh.edu /math/gjennings/perron.html (129 words)

	Transactions of the American Mathematical Society
		Abstract: If is a nonnegative matrix whose associated directed graph is strongly connected, the Perron-Frobenius theorem asserts that
		Our methods show that the Perron-Frobenius theorem is ``really'' about the boundedness of invariant subsets in the Hilbert projective metric.
		Spectral theorem for convex monotone homogeneous maps and ergodic control.
	www.ams.org /tran/2004-356-12/S0002-9947-04-03470-1/home.html (384 words)

	Differential equations, Frobenius theorem and local flows on supermanifolds
		Differential equations, Frobenius theorem and local flows on supermanifolds
		The classical Frobenius theorem, both in its local and global formulations, is generalised to superanalytic supermanifolds.
		As an application, it is proved that a coset space G/H (where both G and H are super Lie groups) is a supermanifold.
	stacks.iop.org /0305-4470/18/417 (201 words)

	A simple proof of the Perron-Frobenius theorem for positive symmetric matrices
		A simple proof of the Perron-Frobenius theorem for positive symmetric matrices
		An elementary proof is given that the statistical mechanical transfer matrix, when symmetric, has a maximum eigenvalue which is non-degenerate and larger than the absolute value of any other eigenvalue.
		In particular, reselling and systematic downloading of files is prohibited.
	stacks.iop.org /0305-4470/9/1281 (211 words)

	Perron-Frobenius theorem for multi-valued mappings, Hiroshi Tateishi
		[5] FUJIMOTO, T., Nonlinear generalization of the Frobenius theorem, J. Math.
		[7] FUJIMOTO, T. and M. MORISHIMA, The Frobenius theorem, its Solow-Samuelso extension and the Kuhn-Tucker theorem, J. Math.
		[16] OSHIME, Y., An extension of Moshima's nonlinear Perron-Frobenius theorem, J. Math.
	projecteuclid.org /getRecord?id=euclid.kmj/1138039594 (388 words)

	question on the integration theorem of Frobenius (Site not responding. Last check: 2007-10-31)
		Subject: question on the integration theorem of Frobenius
		As far as I understand it the Frobenius theorem says that if w is a 1-form then it can be written as w = fdu (f and u are 0-forms, i.e., functions) if and only if w ^ dw =0.
		Now let us assume that for some 1-form w w ^ dw <> 0 and hence one cannot write it as fdu.
	www.lns.cornell.edu /spr/2002-02/msg0039112.html (132 words)

	sylvain perron - ResearchIndex document query (Site not responding. Last check: 2007-10-31)
		invariance theorem holds: Theorem 1 The Frobenius-Perron-Operator (5) is invariant on the function spaces
		Convergence of averages of scaled functions of I(1) linear..
		We prove a generalization of a theorem by Perron[3] about the distribution of quadratic residues
	citeseer.ist.psu.edu /cis?q=Sylvain+Perron (861 words)

	Table of Contents for Geometry of Differential Forms
		The Stokes theorem (in the case of manifolds)
		Integral of differential forms on chains, and the Stokes theorem
		The Hodge theorem and the Hodge decomoposition of differential forms
	www.isbn.nu /toc/0821810456 (294 words)

	THE PERRON (Site not responding. Last check: 2007-10-31)
		The answer to this question is yes, as is shown in problem 3 of Project #8
		Referring to the two matrices above, we find that by direct computation
		If we look back at the statement of the Perron-Frobenius Theorem, we see it guaranteed a positive eigenvalue (with positive eigenvector) with absolute value greater than or equal to that of any other eigenvalue.
	www.dean.usma.edu /departments/math/courses/ma489d/projects/perron.htm (2170 words)

	Tech Report: HPL-BRIMS-2001-12: The Perron-Frobenius Theorem for
		Keyword(s): Collatz-Wielandt property; Hilbert projective metric; nonexpansive function; nonlinear eigenvalue; Perron- Frobenius theorem; strongly connected graph; supereigenspace; topical function
		Abstract:If A is a nonnegative matrix whose associated directed graph is strongly connected, the Perron-Frobenius theorem asserts that A has an eigenvector in the positive cone, (R
		We associate a directed graph to any homogeneous, monotone function, f : (R
	www.hpl.hp.com /techreports/2001/HPL-BRIMS-2001-12.html (124 words)

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