On a generalized core inverse

The paper introduces the concept of a generalized core inverse of a matrix, which extends the notion of the core inverse defined by Baksalary and Trenkler [1]. While the original core inverse is restricted to matrices of index one, the generalized core inverse exists for any square matrix. Several properties of the new concept are identified with the derivations based essentially on partitioned representations of matrices. Some of the features of the generalized core inverse coincide with those attributed to the core inverse, but there are also such which characterize the core inverse only and not its generalization.