Results 131 to 140 of about 477,790 (171)

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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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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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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Joint Spectral Radius

2010
The spectral radius of a square matrix is the absolute value of its largest eigenvalue. The joint spectral radius of two square matrices A and B of the same size, is defined by the following steps:
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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 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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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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SPECTRAL RADIUS, KRONECKER PRODUCTS AND STATIONARITY

Journal of Time Series Analysis, 1992
Abstract. We provide a stochastic proof of the inequality ρ(A⊗A+B⊗B) ≥ρ(A⊗A), where ρ(M) denotes the spectral radius of any square matrix M, i.e. max{|eigenvalues| of M}, and M⊗N denotes the Kronecker product of any two matrices M and N. The inequality is then used to show that stationarity of the bilinear model image will imply stationarity of the ...
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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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Characterizing star factors via the size, the spectral radius or the distance spectral radius of graphs

Discrete Applied Mathematics, 2023
Jianping Li
exaly