mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded...

In mathematics, the joint spectral radius is a generalization of the classical notion of spectral radius of a matrix, to sets of matrices. In recent years...

is the spectral norm. The two values do not coincide in infinite dimensions — see Spectral radius for further discussion. The spectral radius should not...

has spectral radius 2 or at most 2. The graphs with spectral radius 2 form two infinite families and three sporadic examples; if we ask for spectral radius...

in absolute value is strictly smaller than r , |λ| < r. Thus, the spectral radius ρ ( A ) {\displaystyle \rho (A)} is equal to r. If the matrix coefficients...

theory) Cheeger constant (Riemannian geometry) Eigengap Spectral gap (physics) Spectral radius "Impossible-Seeming Surfaces Confirmed Decades After Conjecture"...

magnetic field. The correlation coefficient of a population parameter The spectral radius of a matrix A {\displaystyle A} denoted as ρ ( A ) {\displaystyle \rho...

( ρ ( T ) {\displaystyle \rho (T)} is sometimes used to denote the spectral radius of T {\displaystyle T} ) If λ {\displaystyle \lambda } is an eigenvalue...

above by ‖ W r e c ‖ k {\displaystyle \|W_{rec}\|^{k}} . So if the spectral radius of W r e c {\displaystyle W_{rec}} is γ < 1 {\displaystyle \gamma <1}...

1 are all distinct. That is, the transfer function's spectral radius is 1. If the spectral radius is less than 1, the system is instead asymptotically...

eigenvectors. The spectral radius of a square matrix is the largest absolute value of its eigenvalues. In spectral theory, the spectral radius of a bounded...

conjugate transpose of the matrix A {\displaystyle A} ). In general, the spectral radius of A {\displaystyle A} is bounded above by the operator norm of A {\displaystyle...

(x)} of an element x {\displaystyle x} is non-empty and satisfies the spectral radius formula: sup { | λ | : λ ∈ σ ( x ) } = lim n → ∞ ‖ x n ‖ 1 / n . {\displaystyle...

the maximum absolute value of any eigenvalue. This is known as the spectral radius of the matrix. Let λi be an eigenvalue of an n by n matrix A. The algebraic...

numerical radius is equal to the spectral norm. Still in functional analysis, λ max {\displaystyle \lambda _{\max }} is known as the spectral radius. In the...

differentiable, a sufficient condition for convergence is that the spectral radius of the derivative is strictly bounded by one in a neighborhood of the...

DFS(a)=(n^{*}(a),0,0).} A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator. One way to calculate R 0 {\displaystyle...

standard convergence condition (for any iterative method) is when the spectral radius of the iteration matrix is less than 1: ρ ( D − 1 ( L + U ) ) < 1....

holds. Every normal element is a normaloid element, i.e. the spectral radius r ( a ) {\displaystyle r(a)} equals the norm of a {\displaystyle a}...

{\displaystyle 0\leq p\leq n} , let d p {\displaystyle d_{p}} be the spectral radius of f acting by pullback on the Hodge cohomology group H p , p ( X )...

matrix, that is, the largest singular value of the matrix, that is, the spectral radius of the matrix (these concepts are the same for matrices, but different...

V − 1 {\displaystyle FV^{-1}} with the largest absolute value (the spectral radius of F V − 1 {\displaystyle FV^{-1}} ). Next generation matrices can...

Perth, Australia Jai Shri Ram, a Hindu slogan and greeting Joint spectral radius, in mathematics JSR Corporation [ja; es], a Japanese chemical business...

(functional analysis) Spectral radius, Spectrum of an operator, Spectral theorem Spectral theory of compact operators Spectral theory of normal C*-algebras...

{\displaystyle \|T(t_{0})\|<1} , There exists a t1 > 0 such that the spectral radius of T(t1) is strictly smaller than 1, There exists a p ∈ [1, ∞) such...

number (if it exists) of vertices in a graph whose adjacency matrix has spectral radius exactly ( 1 − α ) / ( 2 α ) {\displaystyle (1-\alpha )/(2\alpha )}...

closely related case, the Perron number of a graph is defined to be the spectral radius of its adjacency matrix. Any Pisot number or Salem number is a Perron...

is equal to the spectral norm. Still in functional analysis, λ max {\displaystyle \lambda _{\max }} is known as the spectral radius. In the context of...

Alexandr (2020-03-01). "Forbidden Subgraphs for Graphs of Bounded Spectral Radius, with Applications to Equiangular Lines". Israel Journal of Mathematics...

Spectral radius ρ ( C ω ) {\displaystyle \rho (C_{\omega })} of the iteration matrix for the SOR method C ω {\displaystyle C_{\omega }} . The plot shows...