Results 261 to 270 of about 66,958 (298)

The generalized spectral radius, numerical radius and spectral norm

Linear and Multilinear Algebra, 1984
Given n×n complex matrices A, C with eigenvalues αj, γj, 1 ⩾ j ⩾ n, respectively, we have the relation where and respectively are the generalized spectral radius, generalized numerical radius and generalized spectral norm of A with respect to C. For C = diag(1,0,…,0), it reduces to the classical relation In this note, we investigate matrices for which .
Chi-Kwong Li, Tin-Yau Tam, Nam-Kiu Tsing
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On the $α$-spectral radius of hypergraphs

CoRR, 2023
For real $α\in [0,1)$ and a hypergraph $G$, the $α$-spectral radius of $G$ is the largest eigenvalue of the matrix $A_α(G)=αD(G)+(1-α)A(G)$, where $A(G)$ is the adjacency matrix of $G$, which is a symmetric matrix with zero diagonal such that for distinct vertices $u,v$ of $G$, the $(u,v)$-entry of $A(G)$ is exactly the number of edges containing both $
Haiyan Guo, Bo Zhou 0007, Bizhu Lin
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Spectral Radius and Radius of Convergence

The American Mathematical Monthly, 1974
(1974). Spectral Radius and Radius of Convergence. The American Mathematical Monthly: Vol. 81, No. 6, pp. 625-627.
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On Permutability and Submultiplicativity of Spectral Radius

Canadian Journal of Mathematics, 1995
AbstractLet r(T) denote the spectral radius of the operator T acting on a complex Hilbert space H. Let S be a multiplicative semigroup of operators on H. We say that r is permutable on 𝓢 if r(ABC) = r(BAC), for every A,B,C ∈ 𝓢. We say that r is submultiplicative on 𝓢 if r(AB) ≤ r(A)r(B), for every A, B ∈ 𝓢.
Longstaff, W. E., Radjavi, H.
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On the joint spectral radius of matrices of order 2 with equal spectral radius

Advances in Computational Mathematics, 2009
Many applications like stability analysis of stochastic dynamical systems, or in approximation theory use the joint spectral radius to verify the convergence or smoothness of subdivision algorithms. The joint spectral radius of two matrices \(A_1,A_2\in \mathbb{R}^{d\times d}\) is \(\mathrm{jsr}(A_1,A_2):=\lim_{n \to \infty}\max \{\| T_1T_2\cdots T_n\|^
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A lower bound for the spectral radius

Proceedings of the American Mathematical Society, 1980
We prove an inequality for a problem of Carathéodory type: given n inner functions m
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The Spectral Radius of infinite Graphs

Bulletin of the London Mathematical Society, 1988
For an infinite graph \(\Gamma\) with vertex set V and finitely bounded valency, the adjacency operator A is well-defined on \(\ell^ 2(V)\) and is bounded and self-adjoint. The spectral radius \(\rho\) (\(\Gamma)\) is the supremum of \(| |\) over \(\| x\| =1\).
Biggs, N.L., Mohar, B., Shawe-Taylor, J.
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Spectral Radius and Degree Sequence

Mathematische Nachrichten, 1988
AbstractFor a nonregular graph there is exactly one value of p such that the p‐mean of its degree sequence is equal to the spectral radius. We try to investigate the structural content of this so‐called spectral mean characteristic; in particular, we characterize the connected graphs of spectral mean characteristic 2.
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ON THE STOCHASTIC SPECTRAL RADIUS FORMULA

The Quarterly Journal of Mathematics, 1995
It is known that if \(\{Y_n\}\) is a stationary sequence of random matrices and \(|\cdot |\) a Banach algebra norm, then \[ \lim_{t \to \infty} {1\over t} \log |X_{0t}|= \gamma\;\text{ a.s.},\tag{1} \] where \(X_{0t} \equiv Y_1 Y_2 \dots Y_t\) and \(\gamma\) is a constant under hypotheses of the 0-1 law. The present paper is devoted to a generalization
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Nested Bounds for the Spectral Radius

SIAM Journal on Numerical Analysis, 1968
It is knowyn [5, Theorem 2.7] that if A > 0 (every element of A is nonnegative), then A has a inonnegative real eigenvalue equal to its spectral radius. If in addition A is irreducible, then this eigeuivalue is positive and simple. If a nonnegative irreducible matrix has k eigenvalues of modulus p(A), then A is said to be k-cyclic if k > I and ...
Hall, C. A., Spanier, Jerome
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