On the minimum vector rank of multigraphs.
On the Monotonity of Incomplete Factorization.
On the optimality and sharpness of Laguerre's lower bound on the smallest eigenvalue of a symmetric positive definite matrix
Lower bounds on the smallest eigenvalue of a symmetric positive definite matrix play an important role in condition number estimation and in iterative methods for singular value computation. In particular, the bounds based on and have attracted attention recently, because they can be computed in operations when is tridiagonal. In this paper, we focus on these bounds and investigate their properties in detail. First, we consider the problem of finding the optimal bound that can be computed...
On the periodic quotient singular value decomposition.
On the polynomial numerical hull of a normal matrix.
On the principal minors of a matrix with a multiple eigenvalue.
On the problem in max algebra: every system of intervals is a spectrum
We consider the two-sided eigenproblem over max algebra. It is shown that any finite system of real intervals and points can be represented as spectrum of this eigenproblem.
On the Rodman-Shalom conjecture regarding the Jordan form of completions of partial upper triangular matrices.
On the separation of eigenvalues by the permutation group
Let A be an invertible 3 × 3 complex matrix. It is shown that there is a 3 × 3 permutation matrix P such that the product PA has at least two distinct eigenvalues. The nilpotent complex n × n matrices A for which the products PA with all symmetric matrices P have a single spectrum are determined. It is shown that for a n × n complex matrix [...] there exists a permutation matrix P such that the product PA has at least two distinct eigenvalues.
On the Sharpness of Some Upper Bounds for the Spectral Radii of S.O.R. Iteration Matrices.
On the signless Laplacian spectral characterization of the line graphs of -shape trees
A graph is determined by its signless Laplacian spectrum if no other non-isomorphic graph has the same signless Laplacian spectrum (simply is ). Let denote the -shape tree obtained by identifying the end vertices of three paths , and . We prove that its all line graphs except () are , and determine the graphs which have the same signless Laplacian spectrum as . Let be the maximum signless Laplacian eigenvalue of the graph . We give the limit of , too.
On the singular decomposition of matrices.
On the singular two-parameter eigenvalue problem.
On the star partial ordering of normal matrices.
On the strong Arnol'd hypothesis and the connectivity of graphs.
On the trace characterization of the joint spectral radius.
On the vectors associated with the roots of max-plus characteristic polynomials
We discuss the eigenvalue problem in the max-plus algebra. For a max-plus square matrix, the roots of its characteristic polynomial are not its eigenvalues. In this paper, we give the notion of algebraic eigenvectors associated with the roots of characteristic polynomials. Algebraic eigenvectors are the analogues of the usual eigenvectors in the following three senses: (1) An algebraic eigenvector satisfies an equation similar to the equation for usual eigenvectors. Under a suitable assumption,...
On the weak robustness of fuzzy matrices
A matrix in -algebra (fuzzy matrix) is called weakly robust if is an eigenvector of only if is an eigenvector of . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an algorithm for checking the weak robustness is described.
On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices.
On uniform symmetrization of analytic matrix functions