Matrix roots of imprimitive irreducible nonnegative matrices
نویسندگان
چکیده
منابع مشابه
Hoffman Polynomials of Nonnegative Irreducible Matrices and Strongly Connected Digraphs
For a nonnegative n× n matrix A, we find that there is a polynomial f(x) ∈ R[x] such that f(A) is a positive matrix of rank one if and only if A is irreducible. Furthermore, we show that the lowest degree such polynomial f(x) with tr f(A) = n is unique. Thus, generalizing the well-known definition of the Hoffman polynomial of a strongly connected regular digraph, for any irreducible nonnegative...
متن کاملSmall Polynomial Matrix Presentations of Nonnegative Matrices
We investigate the use of polynomial matrices to give efficient presentations of nonnegative matrices exhibiting prescribed spectral and algebraic behavior.
متن کاملPerron Vectors of an Irreducible Nonnegative Interval Matrix
As is well known, an irreducible nonnegative matrix possesses a uniquely determined Perron vector. As the main result of this paper we give a description of the set of Perron vectors of all the matrices contained in an irreducible nonnegative interval matrix A. This result is then applied to show that there exists a subset A∗ of A parameterized by n parameters (instead of n2 ones in the descrip...
متن کاملOn Reduced Rank Nonnegative Matrix Factorization for Symmetric Nonnegative Matrices
Let V ∈ R be a nonnegative matrix. The nonnegative matrix factorization (NNMF) problem consists of finding nonnegative matrix factors W ∈ R and H ∈ R such that V ≈ WH. Lee and Seung proposed two algorithms which find nonnegative W and H such that ‖V −WH‖F is minimized. After examining the case in which r = 1 about which a complete characterization of the solution is possible, we consider the ca...
متن کاملInverses of M-type Matrices Created with Irreducible Eventually Nonnegative Matrices
An M-matrix is a matrix that can be expressed as αI − P, where P is entry wise nonnegative and α ≥ ρ(P ). It is well known that the inverse of a nonsingular irreducible M-matrix is positive. In this paper, matrices of the form αI − P, where P is an irreducible eventually nonnegative matrix and α > ρ(P ), are studied. It is shown that if index0(P ) ≤ 1, then there exists a positive number λ such...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.06.005