A class of oscillatory matrices with exponent n−1

Multiplicative Principal-minor Inequalities for a Class of Oscillatory Matrices

A square matrix is said to be totally nonnegative (respectively, positive) if all of its minors are nonnegative (respectively, positive). Determinantal inequalities have been a popular and important subject, especially for positivity classes of matrices such as: positive semidefinite matrices, M−matrices, and totally nonnegative matrices. Our main interest lies in characterizing all of the ineq...

Exponent matrices and their quivers

Exponent matrices appeared in the study of tiled orders over discrete valuation rings. Many properties of such orders are formulated using this notion. We think that such matrices are of interest in them own right, in particular, it is convenient to write finite partially ordered sets (posets) and finite metric spaces as special exponent matrices. Note that when we defined a quiver Q(E) of a re...

Accurate Eigenvectors of Oscillatory Matrices

The purpose of this report is to investigate the possibilities for accurate computation of eigenvectors of (unsymmetric) oscillatory matrices. The goal is to decide what “accurate” means, to determine whether the eigenvectors are determined “accurately” in that sense, and to engineer algorithms that will guarantee that accuracy. It is desirable for the computed eigenvector matrix to inherit the...

On exponent matrices of tiled orders

A ring Λ is called a tiled order if Λ is a prime Noetherian semi-prefect semi-distributive ring with non-zero Jacobson radical. Any tiled order can be constructed from a (non-necessarily commutative) discrete valuation ring and an exponent matrix. The latter means a square integer matrix A = (αps), whose diagonal entries are equal to zero, and for all possible indices i, j, k, the following ine...

Lyapunov Exponent for Products of Random Matrices