Constructions of trace zero symmetric stochastic matrices for the inverse eigenvalue problem
نویسندگان
چکیده
منابع مشابه
Ela Constructions of Trace Zero Symmetric Stochastic Matrices for the Inverse Eigenvalue Problem∗
In the special case of where the spectrum σ = {λ1, λ2, λ3, 0, 0, . . . , 0} has at most three nonzero eigenvalues λ1, λ2, λ3 with λ1 ≥ 0 ≥ λ2 ≥ λ3, and λ1 + λ2 + λ3 = 0, the inverse eigenvalue problem for symmetric stochastic n × n matrices is solved. Constructions are provided for the appropriate matrices where they are readily available. It is shown that when n is odd it is not possible to re...
متن کاملConstructions of trace zero symmetric stochastic matrices for the inverse eigenvalue problem
In the special case of where the spectrum σ = {λ1, λ2, λ3, 0, 0, . . . , 0} has at most three nonzero eigenvalues λ1, λ2, λ3 with λ1 ≥ 0 ≥ λ2 ≥ λ3, and λ1 + λ2 + λ3 = 0, the inverse eigenvalue problem for symmetric stochastic n × n matrices is solved. Constructions are provided for the appropriate matrices where they are readily available. It is shown that when n is odd it is not possible to re...
متن کاملSome results on the symmetric doubly stochastic inverse eigenvalue problem
The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$, to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$. If there exists an $ntimes n$ symmetric doubly stochastic ...
متن کاملOn the nonnegative inverse eigenvalue problem of traditional matrices
In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کاملThe inverse eigenvalue problem for symmetric anti-bidiagonal matrices
X iv :m at h/ 05 05 09 5v 1 [ m at h. R A ] 5 M ay 2 00 5 The inverse eigenvalue problem for symmetric anti-bidiagonal matrices Olga Holtz Department of Mathematics University of California Berkeley, California 94720 USA March 6, 2008
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: The Electronic Journal of Linear Algebra
سال: 2002
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1089