A necessary and sufficient condition for stability of the convex combination of polynomials
A necessary and sufficient eigenvector condition for a connected graph to be bipartite.
A new family of spectrally arbitrary ray patterns
An ray pattern is called a spectrally arbitrary ray pattern if the complex matrices in give rise to all possible complex polynomials of degree . In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an irreducible spectrally arbitrary ray pattern is . In this paper, we introduce a new family of spectrally arbitrary ray patterns of order with exactly nonzeros.
A new inclusion interval for the real eigenvalues of real matrices
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 the effectiveness...
A new proof of a theorem about generalized orthogonal polynomials.
A new upper bound for the Laplacian spectral radius of a graph.
A Newton Iteration Process for Inverse Eigenvalue Problems.
A note on a distance bound using eigenvalues of the normalized Laplacian matrix.
A note on estimate of the spectral radius of symmetric matrices
A note on estimates for the spectral radius of a nonnegative matrix.
A note on nonnegative matrices
A Note on Sub-Multiplicative Norms.
A note on the convexity of the realizable set of eigenvalues for nonnegative symmetric matrices.
A note on the largest eigenvalue of non-regular graphs.
A note on the spectra of tridiagonal matrices.
A parameterized lower bound for the smallest singular value.
A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory
A refined unsymmetric Lanczos eigensolver for computing accurate eigentriplets of a real unsymmetric matrix.
A refinement of an inequality of Johnson, Loewy and London on nonnegative matrices and some applications.
A relation between the multiplicity of the second eigenvalue of a graph Laplacian, Courant's nodal line theorem and the substantial dimension of tight polyhedral surfaces.