Generalized numerical ranges, joint positive definiteness and multiple eigenvalues
نویسندگان
چکیده
منابع مشابه
Generalized numerical ranges of matrix polynomials
In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.
متن کاملPositive Definiteness of Generalized Homogeneous Functions
Identification of positive definiteness of functions is crucial in control theory. However for generalized homogeneous functions, there does not exist an effective method to identify the positive definiteness. In this paper, we consider Lipschitz continuous generalized homogeneous functions. For the functions, we propose a new method to identify the positive definiteness of the functions. Moreo...
متن کاملMultiplicities, Boundary Points, and Joint Numerical Ranges
The multiplicity of a point in the joint numerical range W (A1, A2, A3) ⊆ R is studied for n×n Hermitian matrices A1, A2, A3. The relative interior points of W (A1, A2, A3) have multiplicity greater than or equal to n−2. The lower bound n−2 is best possible. Extreme points and sharp points are studied. Similar study is given to the convex set V (A) := {xT Ax : x ∈ R, x x = 1} ⊆ C, where A ∈ Cn×...
متن کاملGeneralized Numerical Ranges and Quantum Error Correction
For a noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the joint rank-k numerical range associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint rank k-numerical range are obtained and their implications to quantum computing are discussed. It is shown that for a given k if the dimension of the un...
متن کاملQuantum error correction and generalized numerical ranges
For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint higher rank numerical ranges are obtained and their implications to quantum computing are discussed. It is shown that if the dimension of the underlying Hilbert ...
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: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03781-7