The Star of David Rule

TL;DR

This paper introduces the concept of SDR-matrices, explores their properties, and presents conjectures about their behavior, including the potential preservation of the SDR property under matrix inversion.

Contribution

It proposes the new concept of SDR-matrices, discusses their fundamental properties, and formulates conjectures about their structural characteristics and behavior.

Findings

Defined the concept of SDR-matrices

Analyzed basic properties of SDR-matrices

Proposed conjectures on SDR-matrices and their inverses

Abstract

In this note, a new concept called {\em $SDR$-matrix} is proposed, which is an infinite lower triangular matrix obeying the generalized rule of David star. Some basic properties of $SDR$-matrices are discussed and two conjectures on $SDR$-matrices are presented, one of which states that if a matrix is a $SDR$-matrix, then so is its matrix inverse (if exists).