2012/10/05 by Fapeng Du, Du, Fapeng, Yifeng Xue +1
Computer Science · Mathematics · #15A09 #65F20 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Rings and Algebras (math.RA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1210.1627
openalex publication_date 2012/10/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let \R be a ring with unit 1 and a∈ \R, a=a+δa∈ \R such that a^# exists. In this paper, we mainly investigate the perturbation of the group inverse a^# on \R. Under the stable perturbation, we obtain the explicit expressions of a^#. The results extend the main results in Xue (2007), and Xue and Chen (2007) and some related results in Xue (2012). As an application, we give the representation of the group inverse of the matrix d&b c&0 on the ring \R for certain d, b, c∈\R.