CHARACTERIZATION OF PRIMITIVE EXTREMAL MATRICES

摘要

Let D（n,d）={A|A is an n×n primitive matrix with d positive diagonal elements}. Itis well known that γ（A）≤2n-d-1 for A∈D（n,d）. Suppose D₁（n,d）={A∈D（n,d） |γ（A）=2n-d-1} is the set of extremal matrices in D（n,d）. This paper gives a characteriza-tion of the set D₁（n,d）.