is not potentially nilpotent for
An sign pattern is said to be potentially nilpotent if there exists a nilpotent real matrix with the same sign pattern as . Let be an sign pattern with such that the superdiagonal and the entries are positive, the
sign pattern matrices that allow orthogonality
A sign pattern is a sign pattern if has no zero entries. allows orthogonality if there exists a real orthogonal matrix whose sign pattern equals . Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for sign patterns with to allow orthogonality.
A basis of the conjunctively polynomial-like Boolean functions.
A bound for the spectral variation of two matrices.
A Brauer’s theorem and related results
Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system...
A characterization of strong regularity of interval matrices.
A common recursion for Laplacians of matroids and shifted simplicial complexes.
A Computational Method for Eigenvalues and Eigenvectors of a Matrix with Real Eigenvalues.
A convergence criterion for multiple ratios
A Convergent Jacobi Method for Solving the Eigenproblem of Arbitrary Real Matrices.
A deflation formula for tridiagonal matrices
An explicit formula for the deflation of a tridiagonal matrix is presented. The resulting matrix is again tridiagonal.
A fast algorithm for solving regularized total least squares problems.
A formula for all minors of the adjacency matrix and an application
We supply a combinatorial description of any minor of the adjacency matrix of a graph. This description is then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of a graph G, whenever A(G) is invertible, where G is formed by replacing the edges of a tree by path bundles.
A formula for the eigenvalues of a compact operator
A geometric maximization problem
A geometric proof of the Perron-Frobenius theorem.
We obtain an elementary geometrical proof of the classical Perron-Frobenius theorem for non-negative matrices A by using the Brouwer fixed-point theorem and by studying the dynamics of the action of A on convenient subsets of Rn.
A. Horn's result on matrices with prescribed singular values and eigenvalues.
A Jacobi Type Method for Complex Symmetric Matrices.
A lower bound sequence for the minimum eigenvalue of Hadamard product of an -matrix and its inverse
We propose a lower bound sequence for the minimum eigenvalue of Hadamard product of an -matrix and its inverse, in terms of an -type eigenvalues inclusion set and inequality scaling techniques. In addition, it is proved that the lower bound sequence converges. Several numerical experiments are given to demonstrate that the lower bound sequence is sharper than some existing ones in most cases.
A matrix inequality for Möbius functions.