Results 21 to 30 of about 1,914,031 (237)
On the minimum number of distinct eigenvalues of a threshold graph [PDF]
Linear Algebra and its Applications, 2022 For a graph $G$, we associate a family of real symmetric matrices, $S(G)$, where for any $A\in S(G)$, the location of the nonzero off-diagonal entries of $A$ are governed by the adjacency structure of $G$. Let $q(G)$ be the minimum number of distinct eigenvalues over all matrices in $S(G)$.
Shaun Fallat, Seyed Ahmad Mojallal
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An Invariant Fomulation of the New Maximum-Minimum Theory of Eigenvalues [PDF]
Indiana University Mathematics Journal, 1966 Alexander Weinstein
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Graph diameter, eigenvalues, and minimum-time consensus [PDF]
Automatica, 2013 We consider the problem of achieving average consensus in the minimum number of linear iterations on a fixed, undirected graph. We are motivated by the task of deriving lower bounds for consensus protocols and by the so-called "definitive consensus conjecture" which states that for an undirected connected graph G with diameter D there exist D matrices ...
Julien M. Hendrickx +3 more
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On the minimum number of eigenvalues of trees of diameter seven [PDF]
The underlying graph $G$ of a symmetric matrix $M=(m_{ij})\in \mathbb{R}^{n\times n}$ is the graph with vertex set $\{v_1,\ldots,v_n\}$ such that a pair $\{v_i,v_j\}$ with $i\neq j$ is an edge if and only if $m_{ij}\neq 0$. Given a graph $G$, let $q(G)$ be the minimum number of distinct eigenvalues in a symmetric matrix whose underlying graph is $G$. A
Luiz Emílio Allem +2 more
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Signal Bandwidth Impact on Maximum-Minimum Eigenvalue Detection
IEEE Communications Letters, 2015 The impact of the signal bandwidth and observation bandwidth on the detection performance of the maximum-minimum eigenvalue detector is studied in this letter. The considered signals are the Gaussian signals. The optimum ratio between the signal and the observation bandwidth is analytically proven to be 0.5 when reasonable values of the system ...
Mohamed Hamid +2 more
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A lower bound for the minimum eigenvalue of the Hadamard product of matrices
Linear Algebra and its Applications, 2003 Let \(A\) and \(B\) be \(M\)-matrices of the same size \(n\times n\). That is, they are invertible, their off-diagonal entries are non-positive, and the inverses have all entries nonnegative. A number of other equivalent characterizations indicates the significance of this class.
Chen Shen-can
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Inequalities for the minimum eigenvalue of M-matrices
The Electronic Journal of Linear Algebra, 2010 Let A be a nonsingular M-matrix, and τ(A) denote its minimum eigenvalue. Shivakumar et al. [SIAM J. Matrix Anal. Appl., 17(2):298-312, 1996] presented some bounds of τ(A) when A is a weakly chained diagonally dominant M-matrix. The present paper establishes some new bounds of τ(A) for a general nonsingular M-matrix A.
Gui-xian Tian, Tingzhu Huang
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Minimum number of distinct eigenvalues of graphs [PDF]
The Electronic Journal of Linear Algebra, 2013 The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph $G$, is denoted by $q(G)$. Using other parameters related to $G$, bounds for $q(G)$ are proven and then applied to deduce further properties of $q(G)$. It is shown that there is a great number of graphs $G$ for which $q(G)=2$.
Ahmadi, Bahman +5 more
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Extended Perron complements of M-matrices
AIMS Mathematics, 2023 This paper aims to consider the extended Perron complements for the collection of M-matrices. We first exhibit the connection between the extended Perron complements of M-matrices and nonnegative matrices.
Qin Zhong, Chunyan Zhao
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