Results 251 to 260 of about 1,235,690 (292)

ON THE SIZE, SPECTRAL RADIUS, DISTANCE SPECTRAL RADIUS AND FRACTIONAL MATCHINGS IN GRAPHS

Bulletin of the Australian Mathematical Society, 2023
AbstractWe first establish a lower bound on the size and spectral radius of a graph G to guarantee that G contains a fractional perfect matching. Then, we determine an upper bound on the distance spectral radius of a graph G to ensure that G has a fractional perfect matching.
SHUCHAO LI, SHUJING MIAO, MINJIE ZHANG
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On an inequality for spectral radius

Linear and Multilinear Algebra, 1996
In this note we first extend and then give a related result to an inequality involving the spectral radius of nonnegative matrices that recently appeared in the literature.
Mond, Bertram, Pečarić, Josip
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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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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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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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Local Spectral Radius Preservers

Integral Equations and Operator Theory, 2013
Let \(X\) be an infinite-dimensional complex Banach space and \(\mathcal B(X)\) the space of all bounded operators on \(X\). The authors show that, if \(\varphi\) is a surjective map on \(\mathcal B(X)\) such that \(\mathrm r_{T-S}(x)=0\) if and only if \(\mathrm r_{\varphi(T)-\varphi(S)}(x)=0\) for every \(x\in X\) and \(S,T\in\mathcal B(X)\), then ...
Bourhim, Abdellatif, Mashreghi, Javad
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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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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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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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