On the matrix equation \(A^k=J-I\)
type: Item
instance of: scholarly article
title: On the matrix equation \(A^k=J-I\)
zbMATH Open document ID: 0938.15008
DOI: 10.1016/S0024-3795(99)00021-X
author: Yaokun Wu
author: Qiao Li
author: Xuyan Huang
published in: Linear Algebra and its Applications
publication date: 1999-11-29T00:00:00Z
review text: The paper deals with the (0,1)-matrix equation (1) \(X^k= L_n\), where \(k\) is a positive integer, the main diagonal of the \(n\times n\) matrix \(L_n\) is zero and the off-diagonal elements of \(L_n\) are equal to 1. It is known that equation (1) is solvable if and only if \(k\) is odd and \(n=d^k+1\) for an integer \(d\geq 0\). The authors present the complete solution for the case \(d=2\). Several open problems are also posed.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 1371404
zbMATH Keywords: closed form solution
zbMATH Keywords: (0,1)-matrix equation
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1371404