Some new results on determinantal inequalities and applications.
Li, Hou-Biao, Huang, Ting-Zhu, Li, Hong (2010)
Journal of Inequalities and Applications [electronic only]
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Li, Hou-Biao, Huang, Ting-Zhu, Li, Hong (2010)
Journal of Inequalities and Applications [electronic only]
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Feng Wang, Deshu Sun (2016)
Open Mathematics
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Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.
Cheng, Guang-Hui, Cheng, Xiao-Yu, Huang, Ting-Zhu, Tam, Tin-Yau (2005)
Applied Mathematics E-Notes [electronic only]
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Xiao-Dong Zhang, Rong Luo (2002)
Czechoslovak Mathematical Journal
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We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.
Ranjit Mehatari, M. Rajesh Kannan (2021)
Czechoslovak Mathematical Journal
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For a given complex square matrix with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first, we derive bounds for the second largest and the smallest eigenvalues of adjacency matrices of -regular graphs. Then we establish some bounds for the second largest and the smallest eigenvalues of the normalized adjacency matrices of graphs and the second smallest and the largest eigenvalues of the Laplacian matrices of graphs. The sharpness of these bounds...
Francesco Tudisco (2015)
Special Matrices
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We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector...
Miroslav Fiedler (1977)
Mathematica Slovaca
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Yinghua Wang, Xinnian Song, Lei Gao (2023)
Czechoslovak Mathematical Journal
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By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type -matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate...