Alternative algebraic perturbation expressions for the core-EP inverse of a matrix

Several new algebraic perturbation formulas for the core-EP inverse of matrix A are developed in this pfaper and the nonsingular matrix involved depends on a basis for the nullspace of \((A^k)^*\) ${(A^k)}^{\ast }$ where k is the index of A. In particular, the algebraic perturbation expressions built upon the QR factorization of \(A^k\) $A^k$ for the core-EP inverse are presented. Some of these algebraic perturbation formulas are further simplified for a special case when the index of the matrix is one. Numerical examples are included to illustrate the use of these expressions for the computation of the core-EP inverse and the core inverse.