Explicit Eigen vectors Formulae for Lower Doubly Companion Matrices

Wiwat Wanicharpichat

Abstract

Butcher and Wright [1] used doubly companion matrices as a tool to analyze numerical methods and some general linear methods property. In this paper, we considered a lower doubly companion matrix and prove that any lower doubly companion matrix (LDCM) are similar to a companion matrix. We obtain the LDCM, the explicit form of eigenvectors of the sum of two LDCMs, the explicit form of the upper doubly companion matrix (UDCM), and the explicit form of the sum of two UDCMs.