Faculty Publications

Title

Unitary Matrix Digraphs and Minimum Semidefinite Rank

SelectedWorks Author Profiles:

Lon Mitchell

Document Type

Article

Publication Date

2008

ISSN

0024-3795

Abstract

For an undirected simple graph G, the minimum rank among all positive semidefinite matrices with graph G is called the minimum semidefinite rank (msr) of G. In this paper, we show that the msr of a given graph may be determined from the msr of a related bipartite graph. Finding the msr of a given bipartite graph is then shown to be equivalent to determining which digraphs encode the zero/nonzero pattern of a unitary matrix. We provide an algorithm to construct unitary matrices with a certain pattern, and use previous results to give a lower bound for the msr of certain bipartite graphs.

Publisher

Elsevier

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