Largest absolute value of an operator's eigenvalues
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In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues.[1] More generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectrum. The spectral radius is often denoted by ρ(·).
^Gradshteĭn, I. S. (1980). Table of integrals, series, and products. I. M. Ryzhik, Alan Jeffrey (Corr. and enl. ed.). New York: Academic Press. ISBN 0-12-294760-6. OCLC 5892996.
mathematics, the spectralradius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectralradius of a bounded...
In mathematics, the joint spectralradius is a generalization of the classical notion of spectralradius of a matrix, to sets of matrices. In recent years...
norm is the spectral norm. (The two values do not coincide in infinite dimensions — see Spectralradius for further discussion.) The spectral norm of a...
has spectralradius 2 or at most 2. The graphs with spectralradius 2 form two infinite families and three sporadic examples; if we ask for spectral radius...
eigenvectors. The spectralradius of a square matrix is the largest absolute value of its eigenvalues. In spectral theory, the spectralradius of a bounded...
above by ‖ W r e c ‖ k {\displaystyle \|W_{rec}\|^{k}} . So if the spectralradius of W r e c {\displaystyle W_{rec}} is γ < 1 {\displaystyle \gamma <1}...
(functional analysis) Spectralradius, Spectrum of an operator, Spectral theorem Spectral theory of compact operators Spectral theory of normal C*-algebras...
is equal to the spectral norm. Still in functional analysis, λ max {\displaystyle \lambda _{\max }} is known as the spectralradius. In the context of...
standard convergence condition (for any iterative method) is when the spectralradius of the iteration matrix is less than 1: ρ ( D − 1 ( L + U ) ) < 1....
differentiable, a sufficient condition for convergence is that the spectralradius of the derivative is strictly bounded by one in a neighborhood of the...
(x)} of an element x {\displaystyle x} is non-empty and satisfies the spectralradius formula: sup { | λ | : λ ∈ σ ( x ) } = lim n → ∞ ‖ x n ‖ 1 / n . {\displaystyle...
conjugate transpose of the matrix A {\displaystyle A} ). In general, the spectralradius of A {\displaystyle A} is bounded above by the operator norm of A {\displaystyle...
magnetic field. The correlation coefficient of a population parameter The spectralradius of a matrix A {\displaystyle A} denoted as ρ ( A ) {\displaystyle \rho...
DFS(a)=(n^{*}(a),0,0).} A basic reproduction number can be calculated as the spectralradius of an appropriate functional operator. One way to calculate R 0 {\displaystyle...
numerical radius is equal to the spectral norm. Still in functional analysis, λ max {\displaystyle \lambda _{\max }} is known as the spectralradius. In the...
Alexandr (2020-03-01). "Forbidden Subgraphs for Graphs of Bounded SpectralRadius, with Applications to Equiangular Lines". Israel Journal of Mathematics...
C*-identity is a very strong requirement. For instance, together with the spectralradius formula, it implies that the C*-norm is uniquely determined by the...
1 are all distinct. That is, the transfer function's spectralradius is 1. If the spectralradius is less than 1, the system is instead asymptotically...
matrix, that is, the largest singular value of the matrix, that is, the spectralradius of the matrix (these concepts are the same for matrices, but different...
_{1}-\lambda _{2}} is called the spectral gap and it is related to the expansion of G. It is also useful to introduce the spectralradius of A {\displaystyle A}...
documents describing proposed additions to the Java platform Joint spectralradius, in mathematics Jonathan's Space Report, an online newsletter Journal...
convergence condition was formulated by Johnson et al. in 2006, when the spectralradius of the matrix ρ ( I − | D − 1 / 2 A D − 1 / 2 | ) < 1 {\displaystyle...
been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making...
operator norm of a normal operator equals its numerical radius[clarification needed] and spectralradius. A normal operator coincides with its Aluthge transform...
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