The pseudo core inverse of a companion matrix

• Autor(a) principal: Gao, Yuefeng
• Data de Publicação: 2018
• Outros Autores: Chen, Jianlong, Patrício, Pedro, Wang, Dingguo
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/64252
• topic: Pseudo core inverse; Core inverse; Core-EP inverse; Companion matrix; Toeplitz matrix; Ciências Naturais::Matemáticas; Science & Technology

The notion of core inverse was introduced by Baksalary and Trenkler for a complex matrix of index 1. Recently, the notion of pseudo core inverse extended the notion of core inverse to an element of an arbitrary index in *-rings; meanwhile, it characterized the core-EP inverse introduced by Manjunatha Prasad and Mohana for complex matrices, in terms of three equations. Many works have been done on classical generalized inverses of companion matrices and Toeplitz matrices. In this paper, we discuss existence criteria and formulae of the pseudo core inverse of a companion matrix over a *-ring. A {1, 3}-inverse of a Toeplitz matrix plays an important role in that process.