# Secondary range symmetric matrices

## TL;DR

This paper introduces and explores the properties of secondary range symmetric matrices and their generalized inverses.

## Contribution

The paper introduces secondary range symmetric matrices and provides new characterizations and conditions for their generalized inverses.

## Key findings

- Secondary range symmetric matrices differ from range symmetric matrices and those over Minkowski space.
- Necessary and sufficient conditions for a secondary range symmetric matrix to have a secondary generalized inverse are established.

## Abstract

The concept of secondary range symmetric matrices are introduced here. Some characterizations as well as the equivalent conditions for a range symmetric matrix to be secondary range symmetric matrix is given. The idea of range symmetric matrices, range symmetric matrices over Minkowski space and secondary range symmetric matrices are different, and is depicted with the help of suitable examples. Finally, a necessary and sufficient condition for a secondary range symmetric matrix to have a secondary generalized inverse has been obtained.