# An observation on the determinant of a Sylvester-Kac type matrix

## TL;DR

This paper proves a conjecture about the determinant of a Sylvester-Kac type matrix using a lesser-known result and explores an extension of this determinant property.

## Contribution

It introduces a novel proof of a conjecture related to Sylvester-Kac matrices and extends the result to a broader class of matrices.

## Key findings

- Confirmed the conjecture on the determinant of Sylvester-Kac matrices.
- Extended the determinant result to a more general matrix class.
- Provided a new proof leveraging a lesser-known mathematical result.

## Abstract

Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix and consider an extension of it.