Acute perturbation of the group inverse

作者：Wei, Yimin^*

来源：Linear Algebra and Its Applications, 2017, 534: 135-157.

DOI：10.1016/j.laa.2017.08.009

• Group inverse
• Acute perturbation
• Upper bound
• Spectral radius
• Oblique projection

For any n x n complex matrix A, let A(g) be the group inverse of A. When A is singular, a matrix B = A + E is said to be an acute perturbation of A, if parallel to E parallel to is small and the spectral radius rho(BgB - A(g)A) < 1. The acute perturbation coincides with the stable perturbation of the group inverse, if the matrix B satisfies condition.
R(B) boolean AND N(A) = {0}, N(B) boolean AND R(A) = {0}
which was introduced by Castro-Gonzalez et al. (2008) [8]. Furthermore, several examples are provided to illustrate the acute perturbation of the group inverse.

• 出版日期2017-12-1
• 单位复旦大学