The Bott-Duffin drazin inverse and its application

TL;DR

This paper introduces the Bott-Duffin Drazin inverse, explores its properties, and applies it to find minimum P-norm solutions of matrix equations, extending classical inverse concepts.

Contribution

It defines the new BDD-inverse, characterizes its properties, and develops Cramer's rule for minimum P-norm solutions using this inverse.

Findings

Defined the Bott-Duffin Drazin inverse and analyzed its properties.

Provided characterizations and representations of the BDD-inverse.

Developed Cramer's rule for minimum P-norm solutions of matrix equations.

Abstract

The paper introduce a new type of generalized inverse, called Bott-Duffin drazin inverse (or, in short, BDD-inverse) of a complex square matrix, and give some of its properties, characterizations and representations. Furthermore, We discuss the problem of the minimum P-norm solution of the constraint matrix equation by using the Bott-Duffin drazin inverse, and give Cramer s rule for this minimum P-norm solution.