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Generalized Perron--Frobenius Theorem for Nonsquare Matrices
[article]
2013
arXiv
pre-print
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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. ...
Our paper provides a generalization of the PF Theorem to nonsquare matrices. ...
This paper presents a generalization of the well known Perron-Frobenius (PF) Theorem [14, 26] . ...
arXiv:1308.5915v1
fatcat:cyjixfhlczg6rp4gshb4b7p2va
Generalized Perron–Frobenius Theorem for Multiple Choice Matrices, and Applications
[chapter]
2013
Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
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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. ...
Our paper provides a generalization of the PF Theorem to nonsquare multiple choice matrices. ...
For example, [22, 13] establish the Perron-Frobenius property for almost nonnegative matrices or eventually nonnegative matrices. ...
doi:10.1137/1.9781611973105.35
dblp:conf/soda/AvinBHKLPP13
fatcat:fhzri5ghd5dkxbtxwgctxhrasm
Page 700 of Mathematical Reviews Vol. 48, Issue 3
[page]
1974
Mathematical Reviews
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
The theorem of Perron and Frobenius is inverted in the following three ways. ...
Necessary and sufficient condi- tions are given for this to be possible, in terms of certainly auxiliary (nonsquare) matrices over P having maximal
rank. G. M. Bergman (Berkeley, Calif.) ...
Spectral properties of rational matrix functions with nonnegative realizations
1998
Linear Algebra and its Applications
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W(I) = C(1 -A))'B for 1.6 o(A)) vanishing at infinity, then Y(W) := inf{r 2 0: W has no poles i, with r < [Ai} is a pole of Wand r(A) := spectral radius of A is an eigenvalue of A. ...
We characterize the order of these poles in the spirit of Rothblum's index theorem, namely as the length of the longest chains of singular vertices in the reduced graph of A with a suitable new access ...
Acknowledgements The authors are indebted to a referee for his/her careful work and useful suggestions. which improved the presentation of the results. ...
doi:10.1016/s0024-3795(97)10034-9
fatcat:rnrbqwew7ze2jj6uunnpemvtya
Eigenvalues and singular values of certain random matrices
1990
Journal of Computational and Applied Mathematics
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Implications for the choice of test matrices for numerical algorithms are discussed and some other applications mentioned. ...
This is that, typically, the dominant (Perron) eigenvalue of these matrices is much larger than the magnitudes of the others, especially for large matrices. ...
Introduction Matrices for testing numerical algorithms are often generated randomly. ...
doi:10.1016/0377-0427(90)90025-u
fatcat:bnxjyxbqgfespj7zyb65g65gze
Assessing the similarity of real matrices with arbitrary shape
[article]
2024
arXiv
pre-print
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Methods proposed for comparing vectors, such as cosine similarity, can be readily generalized to matrices. However, this approach usually neglects the inherent two-dimensional structure of matrices. ...
We conclude that SAS is a suitable measure for quantifying the shared structure of matrices with arbitrary shape. ...
Human Brain Project SGA3); the Ministry of Culture and Science of the State of North Rhine-Westphalia, Germany (NRW-network "iBehave", grant number: NW21-049); the Joint Lab "Supercomputing and Modeling for ...
arXiv:2403.17687v1
fatcat:zrw55igpgfccjc7r3mstqohepm
Two-dimensional quantum compass model in a staggered field: some rigorous results
2011
Chinese Physics B
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Using the Perron-Fröbenius theorem and the reflection positivity method, we rigorously determine the low energy spectrum of this model and its global ground state Ψ 0 . ...
For such a matrix, the well-known Perron-Fröbenius theorem in matrix theory is applicable. ...
Such a change is required in order to use the Perron-Fröbenius theorem. ...
doi:10.1088/1674-1056/20/1/017503
fatcat:yrumozhxjvgulfgxxiyznu3cbu
Author index for volumes 101–140
1990
Linear Algebra and its Applications
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CAROLYN A. and JOHNSON,
CHARLES R.: A Combinatorial Converse
to the Perron-Frobenius
Theorem,
136: 173
ESPAROL, FRANCISCO MARCELLAN and GON-
~~LEZ, ISABEL RODRIGUEZ: A Class of
Matrix Orthogonal ...
, 126:87 SZULC, TOMASZ: A Contribution to the Theory of P-Matrices: 139:217 SZULC, TOMASZ: A Criterion for the Nonsingularity of Matrices, 136:299 SZULC, TOMASZ: A Lower Bound for the Perron Root of a ...
doi:10.1016/0024-3795(88)90255-8
fatcat:asw7k2yglfhazbmw4ynl4evwde
On the Convergence of Randomized and Greedy Relaxation Schemes for Solving Nonsingular Linear Systems of Equations
[article]
2022
arXiv
pre-print
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We extend results known for the randomized Gauss-Seidel and the Gauss-Southwell methods for the case of a Hermitian and positive definite matrix to certain classes of non-Hermitian matrices. ...
A major result is that the best convergence bounds that we obtain for the expected values in the randomized algorithm are as good as the best for the deterministic, but more costly algorithms of Gauss-Southwell ...
We want to thank Karsten Kahl from University of Wuppertal for sharing his Matlab implementations constructing convection-diffusion matrices with us. ...
arXiv:2209.03757v1
fatcat:evvgdhyxmzfcvgi6e7xem4udjm
Author index for volumes 101–140
1990
Linear Algebra and its Applications
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CHARLES R.: A Combinatorial
Converse
to the
Perron-Frobenius
Theorem,
136:173
ESPA~OL, FRANCISCO MARCEL~~N and GON-
~~LEZ, ISABEL RODR~CUEZ: A Class of
Matrix Orthogonal
Polynomials
on the ...
, 126:87 SZULC, TOMASZ: A Contribution to the Theory of P-Matrices: 139:217 SZULC, TOMASZ: A Criterion for the Nonsingularity of Matrices, 136:209 SZULC, TOMASZ: A Lower Bound for the Perron Root of a ...
doi:10.1016/0024-3795(90)90235-5
fatcat:el6gaav7ifggxebdi2vito5ox4
Author index to volumes 301–400
2005
Linear Algebra and its Applications
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Hurman, Perron-Frobenius theorem for matrices with some negative entries 328 (2001) 57 Tarragona, S., see Puerta, F. 379 (2004) 329 Tasche, M., see Plonka, G. 394 (2005) 309 Teimoori, H., see Bayat, M. ...
Lamberson, A Perron Theorem for positive componentwise bilinear maps 396 (2005) 259 Casas, F., see Blanes, S. 378 (2004) 135 Casciola, G., F. Fabbri and L.B. ...
doi:10.1016/s0024-3795(05)00125-4
fatcat:mrc33u36wnh57lis5jwcb7bmaa
The Collatz-Wielandt quotient for pairs of nonnegative operators
[article]
2020
arXiv
pre-print
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In this paper we consider two versions of the Collatz-Wielandt quotient for a pair of nonnegative operators A,B that map a given pointed generating cone in the first space into a given pointed generating ...
In this paper we treat the two important cases: a pair of rectangular nonnegative matrices and a pair completely positive operators. ...
We say that Y is a generalized Perron-Frobenius vector or weak generalized Perron-Frobenius vector if
( 21 ) 21 A(Y ) = ρ(A, B)B(Y ), or A(Y ) =ρ(A, B)B(Y ), Y ∈ H +,n \ {0},respectively.Given a pair ...
arXiv:1710.07402v4
fatcat:juf6wtgzc5b3ndisvzp6yztkyq
Alternating-directional Doubling Algorithm for M-Matrix Algebraic Riccati Equations
2012
SIAM Journal on Matrix Analysis and Applications
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Math., 116 (2010), pp. 553-578) for the same purpose. ...
Also demonstrated is that all three methods are capable of delivering minimal nonnegative solutions with entrywise relative accuracies as warranted by the defining coefficient matrices of an MARE. 2000 ...
By the Perron-Frobenius theorem[8, p.27], there is a positive vector u such that N u = ρ(N )u. ...
doi:10.1137/110835463
fatcat:j6ze3txylvd7jhbtuzauzpgo4q
The square and add Markov chain
[article]
2020
arXiv
pre-print
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Squaring and adding ± 1 mod p generates a curiously intractable random walk. ...
Acknowledgements We thank Amol Aggarwal, Steve Butler, Ron Graham, Bob Guralnick, David Kazhdan, Laurent Miclo, Yuval Peres and Kannan Soundararajan for their help. ...
By the Perron-Frobenius theorem, an aperiodic, irreducible Markov chain has a unique stationary distribution.
Finite fields. This classical subject is exhaustively developed in [13] . ...
arXiv:2008.11253v1
fatcat:4r6cve5rcragbgnvp64bm4qyiq
Veech fibrations
[article]
2023
arXiv
pre-print
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2023 pre-print arXiv:2310.02325v1 fatcat:eatzgi7rvfdbxgc6g5xuuydskm
When the fiber has genus one, these surfaces are elliptic fibrations; for higher genus fibers, they are typically minimal surfaces of general type. ...
We get exact values of the invariants for all known algebraically primitive Teichmüller curves. ...
The Perron-Frobenius eigenvalue is µ = 2 cos( π n ). ...
arXiv:2310.02325v2
fatcat:3atl2bbgorbtvix675zpvmrs2y
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