Abstract
Consideration is given to the relation between the structure of the acyclic binary relation and the adjacency matrix of its corresponding graph. In this case, the existing methods for studying the binary relations and their corresponding graphs in terms of the spectrum, that is, the set of eigenvalues, of the adjacency matrix are inapplicable because for the acyclic relations this matrix is nilpotent and its spectrum is identically zero. Therefore, a more refined characteristic of the matrix is required. The present paper considers the Jordan normal form (JNF) as such.
Similar content being viewed by others
References
Aleskerov, F.T., Threshold Utility, Choice, and Binary Relations, Avtom. Telemekh., 2003, no. 3, pp. 17–41.
Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1988. Translated into English under the title Theory of Matrices, New York: Chelsea, 1959.
Gel’fand, I.M., Lektsii po lineinoi algebre (Lectures in Linear Algebra), Moscow: Dobrosvet, 1998.
Aleskerov, F. and Monjardet, B., Utility Maximization, Choice and Preference, Berlin: Springer, 2002.
Harary, F., Graph Theory, Reading: Addison-Wesley, 1969. Translated under the title Teoriya grafov, Moscow: Mir, 1986.
Author information
Authors and Affiliations
Additional information
Original Russian Text © D.A. Shvarts, 2008, published in Avtomatika i Telemekhanika, 2008, No. 11, pp. 171–177.
Rights and permissions
About this article
Cite this article
Shvarts, D.A. Partial orders and Jordan normal form. Autom Remote Control 69, 1973–1979 (2008). https://doi.org/10.1134/S0005117908110143
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117908110143