Results 21 to 30 of about 394 (72)

Two new eigenvalue localization sets for tensors and theirs applications

Open Mathematics, 2017
A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50).
Zhao Jianxing, Sang Caili
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Eigenvalue Localization Inequalities for Complex Matrices With Order n≥3

Advances in Mathematical Physics
MSC2020 Classification: 15A18, 15A60 ...
Rong Ma, Feng Zhang
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Linear combinations of graph eigenvalues

, 2006
Let F(G) be a fixed linear combination of the k extremal eigenvalues of a graph G and of its complement. The problem of finding max{F(G):v(G)=n} generalizes a number of problems raised previously in the literature. We show that the limit max{F(G):v(G)=n}/
Nikiforov, Vladimir
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Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues

Advances in Nonlinear Analysis, 2018
This paper deals with an eigenvalue problem possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental frequency, are ...
Bandle Catherine, Wagner Alfred
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Inequalities for selected eigenvalues of the product of matrices

, 2019
The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues.
Xi, Bo-Yan, Zhang, Fuzhen
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Maxima Q-index of graphs with forbidden odd cycles [PDF]

, 2014
Let $q\left( G\right) $ be the $Q$-index (the largest eigenvalue of the signless Laplacian) of $G$. Let $S_{n,k}$ be the graph obtained by joining each vertex of a complete graph of order $k$ to each vertex of an independent set of order $n-k.$ The main ...
Yuan, Xiying
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The trace norm of r-partite graphs and matrices

, 2015
The trace norm $\left\Vert G\right\Vert _{\ast}$ of a graph $G$ is the sum of its singular values, i.e., the absolute values of its eigenvalues. The norm $\left\Vert G\right\Vert _{\ast}$ has been intensively studied under the name of graph energy, a ...
Nikiforov, V.
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Further refinements of the Cauchy-Schwarz inequality for matrices [PDF]

, 2014
Let $A, B$ and $X$ be $n\times n$ matrices such that $A, B$ are positive semidefinite. We present some refinements of the matrix Cauchy-Schwarz inequality by using some integration techniques and various refinements of the Hermite--Hadamard inequality ...
Bakherad, Mojtaba
core  

Minimum trace norm of real symmetric and Hermitian matrices with zero diagonal

Special Matrices
We establish tight lower bounds for the trace norm (‖⋅‖1)\left(\Vert \cdot {\Vert }_{1}) of real symmetric and Hermitian matrices with zero diagonal entries in terms of their entrywise L1{L}^{1}-norms (‖⋅‖(1))\left(\Vert \cdot {\Vert }_{\left(1)}).
Einollahzadeh Mostafa, Nematollahi Mohammad Ali   +1 more
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Maximum norms of graphs and matrices, and their complements

, 2013
In this paper, we mainly study the trace norm of the adjacency matrix of a graph, also known as the energy of graph. We give the maximum trace norms for the graph and its complement. In fact, the above problem is stated and solved in a more general setup
Nikiforov, Vladimir, Yuan, Xiying
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