Huanyin Chen

The Two-Weight Core-EP Inverse in a Ring

In this paper, we characterize the two-weight core-EP inverse using the weighted core decomposition and establish its novel representations through the weighted g-Drazin inverse. Furthermore, we define and investigate the weighted core-EP orders within this general setting. These...

Weighted EP elements in rings

We introduce the novel concept of weighted EP elements with respect to two elements in a ring to establish a unified framework that naturally generalizes classical EP elements. We then characterize the fundamental properties of weighted EP elements, demonstrating that many classi...

The Core Inverse of the Anti-Triangular Block Matrix over Rings

In this paper, we investigates the core inverse of the anti-triangular block matrix $M=\left( \begin{array}{cc} A&B\\ C&0 \end{array} \right)$ over a ring. We derive new explicit representations for the core inverse of $M$ under specific conditions. In particular, the EP property...

The Core Inverse of Block Anti-Triangular Matrices with Product Subblocks

We present novel explicit representations for the core inverse of block anti-triangular matrices involving core invertible product subblocks. Specifically, the corresponding EP property in each of these cases is examined.

The Generalized Core-EP Inverse for Anti-Triangular Matrices

We investigate the existence and representations of generalized core-EP inverses for a class of anti-triangular matrices over Banach *-algebras. These newly established representations naturally yield innovative formulations for the core and core-EP inverses, providing fresh insi...