On extremal matrices of second largest exponent by Boolean rank

Bijective linear maps on semimodules spa

Bijective linear maps on semimodules spanned by Boolean matrices of fixed rank

✍ Ming-Huat Lim; Sin-Chee Tan 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 180 KB

Let M m,n (B) be the semimodule of all m × n Boolean matrices where B is the Boolean algebra with two elements. Let k be a positive integer such that 2 k min (m, n). Let B (m, n, k) denote the subsemimodule of M m,n (B) spanned by the set of all rank k matrices. We show that if T is a bijective line