Quantum mechanics

Commutative ring

Linguistics

Philosophy

Pure mathematics

Moore–Penrose pseudoinverse

Commutative property

Materials science

Square (algebra)

Eigenvalues and eigenvectors

Inverse

Core (optical fiber)

Square matrix

Matrix (chemical analysis)

Physics

Mathematics

Symmetric matrix

Geometry

Composite material

Combinatorics

Generalized inverse

Algebra over a field

Space (punctuation)

Linear and Multilinear Algebra

In this paper, we present necessary and sufficient conditions for the k-commutative equality A k X = XA k , where X is an outer generalized inverse of the square matrix A. Also, we give new representations for core EP, DMP, and CMP inverses of square matrices as outer inverses with prescribed null space and range.In addition, we characterize the core EP inverse as the solution of a new system of matrix equations.

Characterizations of <i>k</i>-commutative equalities for some outer generalized inverses

Characterizations of k-commutative equalities for some outer generalized inverses