The Minimum Rank of Symmetric Matrices Described by a Graph: A Survey

Date
2007-10-01
Authors
Fallat, Shaun
Hogben, Leslie
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Altmetrics
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Research Projects
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Mathematics
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Abstract

The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. This paper surveys the current state of knowledge on the problem of determining the minimum rank of a graph and related issues.

Description

This is a manuscript of an article from Linear Algebra and its Applications 426 (2007): 558, doi:10.1016/j.laa.2007.05.036. Posted with permission.

Keywords
Minimum rank, Inverse eigenvalue problem, Rank, Graph, Symmetric matrix, Matrix
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