The change of similarity invariants under row perturbations

✍ Scribed by M. Asunción Beitia; Inmaculada de Hoyos; Ion Zaballa

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 296 KB
• Volume: 429
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2008.02.022

✦ Synopsis

The problem of the possible similarity classes of all the matrices obtained by small perturbations on some rows of a given complex square matrix is under consideration. Some necessary conditions on these similarity classes are provided. The near converse problem is also studied: under what conditions can a given collection of polynomials or partitions be the invariant factors or the Weyr characteristic of a matrix obtained by perturbing some rows of a given matrix? A complete answer is provided in some particular cases. The obtained conditions can all be derived from the previously mentioned necessary conditions.