Inverses of M-type matrices created with irreducible eventually nonnegative matrices
نویسندگان
چکیده
منابع مشابه
Inverses 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 کاملEla M ∨ - Matrices : a Generalization of M - Matrices Based on Eventually Nonnegative Matrices
An M ∨-matrix has the form A = sI − B, where s ≥ ρ(B) ≥ 0 and B is eventually nonnegative; i.e., B k is entrywise nonnegative for all sufficiently large integers k. A theory of M ∨-matrices is developed here that parallels the theory of M-matrices, in particular as it regards exponential nonnegativity, spectral properties, semipositivity, monotonicity, inverse nonnegativity and diagonal dominance.
متن کاملMv-matrices: a generalization of M-matrices based on eventually nonnegative matrices
An M∨ matrix has the form A = sI − B, where s ≥ ρ(B) ≥ 0 and B is eventually nonnegative; i.e., Bk is entrywise nonnegative for all sufficiently large integers k. A theory of M∨ matrices is developed here that parallels the theory of M-matrices, in particular as it regards exponential nonnegativity, spectral properties, semipositivity, monotonicity, inverse nonnegativity and diagonal dominance.
متن کاملEventually Nonnegative Matrices and their Sign Patterns
A matrix A ∈ Rn×n is eventually nonnegative (respectively, eventually positive) if there exists a positive integer k0 such that for all k ≥ k0, A ≥ 0 (respectively, A > 0). Here inequalities are entrywise and all matrices are real and square. An eigenvalue of A is dominant if its magnitude is equal to the spectral radius of A. A matrix A has the strong Perron-Frobenius property if A has a uniqu...
متن کاملSpectral Properties of Reducible Nonnegative and Eventually Nonnegative Matrices
Let η = (η1, η2, . . . , ηt) and ν = (ν1, ν2, . . . , νt) be two sequences of nonnegative integers. (Append zeros if necessary to the end of the shorter sequence so that they are the same length.) We say that ν is majorized by η if ∑j l=1 νl ≤ ∑j l=1 ηl for all 1 ≤ j ≤ t and tl=1 νl = ∑t l=1 ηl. We write ν 1 η. Let Γ = (V,E) be a graph where V is a finite vertex set and E ⊆ V ×V is an edge set....
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: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.06.029