What does this research mean for the field?

Novel algebraic perturbation formulas for the m-weak group inverse and m-weak core inverse of a matrix can be derived using a nonsingular matrix contingent upon a basis for the nullspace of (A^k)*. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

May 19, 2026Open Access

Alternative algebraic perturbation expressions for the m-weak group inverse and m-weak core inverse

Key Points

The aim is to develop new algebraic perturbation expressions for the m-weak group inverse and the m-weak core inverse of matrices.
Introduced formulas based on nonsingular matrices connected to the nullspace of (A^k)* where k is the matrix index.
Provided specific formulas for both Drazin and core-EP inverses under particular conditions.
Novel algebraic perturbation formulas for m-weak group and core inverses were established.
Special cases revealed new insights into Drazin and core-EP inverses.

Abstract

This paper presents several novel algebraic perturbation formulas for the m-weak group inverse and the m-weak core inverse of a matrix A. The nonsingular matrix utilized in these formulas is contingent upon a basis for the nullspace of (A^k) *, where k denotes the index of the matrix A. In particular, some new algebraic perturbation formulas for the Drazin inverse and core-EP inverse are presented for a special case.

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Cite This Study

Chen et al. (Wed,) studied this question.

synapsesocial.com/papers/6a0bfe2d166b51b53d379786 https://doi.org/https://doi.org/10.2298/fil2528077c

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