# On special matrices related to Cauchy and Toeplitz matrices

## TL;DR

This paper investigates determinants of matrices related to Cauchy and Toeplitz types and applies these results to find the rank of specific non-square matrices.

## Contribution

It provides new formulas for determinants of certain matrices linked to Cauchy and Toeplitz matrices and uses these to determine ranks of related non-square matrices.

## Key findings

- Derived explicit determinant formulas for related matrices
- Established rank criteria for certain non-square matrices
- Connected determinant properties to matrix rank calculations

## Abstract

In this paper, we are going to calculate the determinant of a certain type of square matrices, which are related to the well-known Cauchy and Toeplitz matrices. Then, we will use the results to determine the rank of special non-square matrices.