Skew-symmetric tridiagonal Bohemian matrices

Principally Unimodular Skew-Symmetric Matrices

A square matrix is principally unimodular if every principal submatrix has determinant 0 or 1. Let A be a symmetric (0; 1)-matrix, with a zero diagonal. A PU-orientation of A is a skew-symmetric signing of A that is PU. If A 0 is a PU-orientation of A, then, by a certain decomposition of A, we can construct every PU-orientation of A from A 0. This construction is based on the fact that the PU-o...

Commutators of Skew-Symmetric Matrices

In this paper we develop a theory for analysing the size of a Lie bracket or commutator in a matrix Lie algebra. Complete details are given for the Lie algebra so(n) of skew symmetric matrices. 1 Norms and commutators in Mn[R] and so(n) This paper is concerned with the following question. Let g be a Lie algebra (Carter, Segal & Macdonald 1995, Humphreys 1978, Varadarajan 1984). Given X,Y ∈ g an...

On skew-symmetric differentiation matrices

The theme of this paper is the construction of finite-difference approximations to the first derivative in the presence of Dirichlet boundary conditions. Stable implementation of splitting-based discretisation methods for the convectiondiffusion equation requires the underlying matrix to be skew symmetric and this turns out to be a surprisingly restrictive condition. We prove that no skewsymmet...

Fine Spectra of Tridiagonal Symmetric Matrices

Inner deflation for symmetric tridiagonal matrices

Suppose that one knows an accurate approximation to an eigenvalue of a real symmetric tridiagonal matrix. A variant of deflation by the Givens rotations is proposed in order to split off the approximated eigenvalue. Such a deflation can be used instead of inverse iteration to compute the corresponding eigenvector. © 2002 Elsevier Science Inc. All rights reserved.