Expressions and characterizations for the Moore-Penrose inverse

Abstract

Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are useful for its computation. We give formulations of them for finite matrices and study the Moore-Penrose inverse of circulant matrices and of distance matrices of certain graphs.

Version accepted in the Electronic Journal of Linear Algebra (Open Access Journal). Differences with respect to v1: Title, Abstract, Keywords, AMS Subject Classification, Sections 1, 2 and 3, and References were modified. Sections 4 and 5 are new

References in corpus (3)

• An inverse formula for the distance matrix of a wheel graph with even number of vertices
• On distance matrices of wheel graphs with odd number of vertices
• When is $(A+B{)}^{†}=A^{†}+B^{†}$?

Cited by in corpus (1)

• Generalized inverses, ideals, and projectors in rings