A characterization of linear operators that preserve isolation numbers

作者：Beasley LeRoy B; Song Seok Zun^*

来源：Mathematical Communications, 2014, 19(2): 363-373.

• Boolean matrix
• Boolean rank
• isolation number
• Boolean linear operator

We obtain characterizations of Boolean linear operators that preserve some of the isolation numbers of Boolean matrices. In particular, we show that the following are equivalent: (1) T preserves the isolation number of all matrices; (2) T preserves the set of matrices with isolation number one and the set of those with isolation number k for some 2 %26lt;= k %26lt;= min{m, n}; (3) for 1 %26lt;= k %26lt;= min{m,n} - 1, T preserves matrices with isolation number k, and those with isolation number k + 1, (4) T maps J to J and preserves the set of matrices of isolation number 2; (5) T is a (P, Q)-operator, that is, for fixed permutation matrices P and Q, m x n matrix X, T(X) = PXQ or, m = n and T(X) = PX(t)Q where X-t is the transpose of X.

• 出版日期2014-12