The peripheral spectrum of a nonnegative matrix
نویسندگان
چکیده
منابع مشابه
Level characteristics corresponding to peripheral eigenvalues of a nonnegative matrix
In this paper, we give necessary and sufficient conditions for a set of Jordan blocks to correspond to the peripheral spectrum of a nonnegative matrix. For each eigenvalue, λ, the λ-level characteristic (with respect to the spectral radius) is defined. The necessary and sufficient conditions include a requirement that the λ-level characteristic is majorized by the λ-height characteristic. An al...
متن کاملMaximal nonnegative perturbation of a nonnegative matrix
is known to be stable if and only if ρ(A) < 1. Models of real world dynamical phenomena often involve positive quantities. A dynamical system (1) is called positive if any trajectory of the system starting in the positive orthant R+ remains in R+. In this case, the matrix A has only real positive entries. In many cases, it may be useful to consider systems with a known “nominal” part A and a un...
متن کاملOn nonnegative operators and fully cyclic peripheral spectrum
In this note the properties of the peripheral spectrumof a nonnegative linear operator A (for which the spectral radius is a pole of its resolvent) in a complex Banach lattice are studied. It is shown, e.g., that the peripheral spectrum of a natural quotient operator is always fully cyclic. We describe when the nonnegative eigenvectors corresponding to the spectral radius r span the kernel N(r ...
متن کاملEla on Nonnegative Operators and Fully Cyclic Peripheral Spectrum
In this note the propertiesof the peripheral spectrum of a nonnegativelinear operator A for which the spectral radius is a pole of its resolvent in a complex Banach lattice are studied. It is shown, e.g., that the peripheral spectrum of a natural quotient operator is always fully cyclic. We describe when the nonnegative eigenvectors corresponding to the spectral radius r span the kernel Nr , A....
متن کاملNonnegative Matrix Factorization of a Correlation Matrix
We present a dedicated algorithm for the nonnegative factorization of a correlation matrix from an application in financial engineering. We look for a low-rank approximation. The origin of the problem is discussed in some detail. Next to the description of the algorithm, we prove, by means of a counter example, that an exact nonnegative decomposition of a general positive semidefinite matrix is...
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: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00616-x