Primitive exponent preservers

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• 作者：LeRoy B. Beasley^a ; ^{leroy.b.beasley@aggiemail.usu.edu" class="auth_mail" title="E-mail the corresponding author} ; Seok-Zun Song^b ; ^{szsong@jejunu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A04 ; 15A86 ; 15B34
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：491
• 期：Complete
• 页码：263-275
• 全文大小：346 K

文摘

Let M_n(B)${\mathcal{M}}_n(\mathbb{B})$ denote the set of n×n$n\times n$(0,1)$(0,1)$-matrices with Boolean arithmetic. The set of primitive matrices of exponent k  , denoted E_k${\mathcal{E}}_k$, is the set of matrices such that A^k$A^k$ has all nonzero entries and A^j$A^j$ has zero entries for all j<k$j<k$. For 3≤k≤n$3\le k\le n$, we characterize those linear operators that map E_k${\mathcal{E}}_k$ to E_k${\mathcal{E}}_k$ and abf0e1a613bf3a8fc" title="Click to view the MathML source">E_k−1${\mathcal{E}}_{k-1}$ to abf0e1a613bf3a8fc" title="Click to view the MathML source">E_k−1${\mathcal{E}}_{k-1}$. We also characterize those linear operators that strongly preserve E_k${\mathcal{E}}_k$ for 3≤k≤n$3\le k\le n$, that is, that map E_k${\mathcal{E}}_k$ to E_k${\mathcal{E}}_k$ and the complement of E_k${\mathcal{E}}_k$ to the complement of E_k${\mathcal{E}}_k$.