scholarly journals A bound on the scrambling index of a primitive matrix using Boolean rank

2009 ◽  
Vol 431 (10) ◽  
pp. 1923-1931 ◽  
Author(s):  
Mahmud Akelbek ◽  
Sandra Fital ◽  
Jian Shen
Keyword(s):  
Primitive Matrix ◽  
Boolean Rank ◽  
Scrambling Index

scholarly journals A bound on the exponent of a primitive matrix using Boolean rank

1995 ◽  
Vol 217 ◽  
pp. 101-116 ◽  
Author(s):  
D.A. Gregory ◽  
S.J. Kirkland ◽  
N.J. Pullman
Keyword(s):  
Primitive Matrix ◽  
Boolean Rank

scholarly journals The scrambling index of symmetric primitive matrices

2010 ◽  
Vol 433 (6) ◽  
pp. 1110-1126 ◽  
Author(s):  
Shexi Chen ◽  
Bolian Liu
Keyword(s):  
Scrambling Index

scholarly journals On extremal matrices of second largest exponent by Boolean rank

2007 ◽  
Vol 422 (1) ◽  
pp. 186-197 ◽  
Author(s):  
Bolian Liu ◽  
Lihua You ◽  
Gexin Yu
Keyword(s):  
Boolean Rank

scholarly journals Non-negative integral matrices with given spectral radius and controlled dimension

2021 ◽  
pp. 1-24
Author(s):  
MEHDI YAZDI
Keyword(s):  
Spectral Radius ◽  
Positive Real Number ◽  
Algebraic Integer ◽  
Log P ◽  
Irreducible Matrix ◽  
Positive Real ◽  
Shift Of Finite Type ◽  
Primitive Matrix ◽  
Integral Matrices ◽  
Perron Number

Abstract A celebrated theorem of Douglas Lind states that a positive real number is equal to the spectral radius of some integral primitive matrix, if and only if, it is a Perron algebraic integer. Given a Perron number p, we prove that there is an integral irreducible matrix with spectral radius p, and with dimension bounded above in terms of the algebraic degree, the ratio of the first two largest Galois conjugates, and arithmetic information about the ring of integers of its number field. This arithmetic information can be taken to be either the discriminant or the minimal Hermite-like thickness. Equivalently, given a Perron number p, there is an irreducible shift of finite type with entropy $\log (p)$ defined as an edge shift on a graph whose number of vertices is bounded above in terms of the aforementioned data.

scholarly journals Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector

2019 ◽  
Vol 23 ◽  
pp. 797-802
Author(s):  
Raphaël Cerf ◽  
Joseba Dalmau
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Branching Process ◽  
Invariant Probability Measure ◽  
Classical Formula ◽  
Multitype Branching Process ◽  
Primitive Matrix ◽  
Watson Process

Let A be a primitive matrix and let λ be its Perron–Frobenius eigenvalue. We give formulas expressing the associated normalized Perron–Frobenius eigenvector as a simple functional of a multitype Galton–Watson process whose mean matrix is A, as well as of a multitype branching process with mean matrix e(A−I)t. These formulas are generalizations of the classical formula for the invariant probability measure of a Markov chain.

scholarly journals CHARACTERIZATIONS OF BOOLEAN RANK PRESERVERS OVER BOOLEAN MATRICES

2014 ◽  
Vol 21 (2) ◽  
pp. 121-128
Author(s):  
Leroy B. Beasley ◽  
Kyung-Tae Kang ◽  
Seok-Zun Song
Keyword(s):  
Boolean Rank
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