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Linear Algebra and its Applications
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.
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Jordan canonical form, directed graph, adjacency matrix
Cardon, D. A., & Tuckfield, B. (2011). The Jordan Canonical Form for a Class of Zero–One Matrices. Linear Algebra and its Applications, 435 (11), 2942-2954. http://dx.doi.org/10.1016/j.laa.2011.05.022
Date Posted: 27 November 2017
This document has been peer reviewed.