Isospectral flows that preserve matrix structure

✍ Scribed by G.M.L. Gladwell; Oscar Rojo

• Book ID: 104036697
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 244 KB
• Volume: 421
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2006.03.042

✦ Synopsis

The matrix A = (a ij )∈S n is said to lie on a strict undirected graph

maintains the spectrum of A. We consider isospectral flows that maintain a matrix A(t) on a given graph G. We review known results for a graph G that is a (generalised) path, and construct isospectral flows for a (generalised) ring, and a star, and show how a flow may be constructed for a general graph. The analysis may be applied to the isospectral problem for a lumped-mass finite element model of an undamped vibrating system. In that context, it is important that the flow maintain other properties such as irreducibility or positivity, and we discuss whether they are maintained.