A new lower bound for the positive semidefinite minimum rank of a graph

作者：Zimmer Andrew M^*

来源：Linear Algebra and Its Applications, 2013, 438(3): 1095-1112.

DOI：10.1016/j.laa.2012.09.001

• Positive semidefinite minimum rank
• Minimum rank
• Sign patterns
• Zero forcing number
• Positive semidefinite zero forcing number
• Ordered set number

The real positive semidefinite minimum rank of a graph is the minimum rank among all real positive semidefinite matrices that are naturally associated via their zero-nonzero pattern to the given graph. In this paper, we use orthogonal vertex removal and sign patterns to improve the lower bound for the real positive semidefinite minimum rank determined by the OS-number and the positive semidefinite zero forcing number.

• 出版日期2013-2-1