A criterion of contractivity for four by four upper-triangular matrices

TL;DR

This paper provides an explicit criterion to determine whether a 4x4 upper-triangular matrix is a contraction under the Euclidean operator norm, aiding in matrix analysis and operator theory.

Contribution

It introduces a novel explicit criterion for contractivity of 4x4 upper-triangular matrices, advancing matrix norm analysis.

Findings

Derived an explicit contractivity criterion for 4x4 upper-triangular matrices

Facilitates easier verification of matrix contractivity

Contributes to the theoretical understanding of matrix norms

Abstract

We establish an explicit criterion for determining whether a $4 \times 4$ upper-triangular matrix is a contraction with respect to the Euclidean operator norm.