On low rank perturbations of matrices
نویسندگان
چکیده
The article is devoted to different aspects of the question: ”What can be done with a matrix by a low rank perturbation?” It is proved that one can change a geometrically simple spectrum drastically by a rank 1 perturbation, but the situation is quite different if one restricts oneself to normal matrices. Also the Jordan normal form of a perturbed matrix is discussed. It is proved that with respect to the distance d(A,B) = rank(A−B) n (here n is the size of the matrices) all almost unitary operators are near unitary.
منابع مشابه
Low rank perturbations of large elliptic random matrices ∗ Sean O ’ Rourke
We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and non-Hermitian random matrices with iid entries. As a consequence, we recover the results of Capitaine, Donati-Martin, and Féral for perturbed Wigner matrices as w...
متن کاملSome Observations on Inverses of Band Matrices and Low Rank Perturbations of Triangular Matrices
متن کامل
Ela on Low Rank Perturbations of Complex Matrices and Some Discrete Metric Spaces∗
In this article, several theorems on perturbations of a complex matrix by a matrix of a given rank are presented. These theorems may be divided into two groups. The first group is about spectral properties of a matrix under such perturbations; the second is about almost-near relations with respect to the rank distance.
متن کاملOn low rank perturbations of complex matrices and some discrete metric spaces
In this article, several theorems on perturbations of a complex matrix by a matrix of a given rank are presented. These theorems may be divided into two groups. The first group is about spectral properties of a matrix under such perturbations; the second is about almost-near relations with respect to the rank distance.
متن کاملOn higher rank numerical hulls of normal matrices
In this paper, some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated. A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given. Moreover, using the extreme points of the numerical range, the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$, where $A_1...
متن کامل