Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

12-2011

Publication Source

Linear Algebra and its Applications

Volume

435

Issue

11

Start Page

2942

Last Page

2954

DOI

10.1016/j.laa.2011.05.022

Abstract

Let f:N→N be a function. Let An=(aij) be the n×n matrix defined by aij=1 if i=f(j) for some i and j and aij=0 otherwise. We describe the Jordan canonical form of the matrix An in terms of the directed graph for which An is the adjacency matrix. We discuss several examples including a connection with the Collatz 3n+1 conjecture.

Copyright/Permission Statement

© <2011>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

Jordan canonical form, directed graph, adjacency matrix

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Date Posted: 27 November 2017

This document has been peer reviewed.