On minimal sets of \((0,1)\)-matrices whose pairwise products form a basis for \(M_{n}(\mathbb{F})\). (English) Zbl 1401.15016
Summary: Three families of examples are given of sets of \((0,1)\)-matrices whose pairwise products form a basis for the underlying full matrix algebra. In the first two families, the elements have rank at most two and some of the products can have multiple entries. In the third example, the matrices have equal rank \(\sqrt{n}\) and all of the pairwise products are single-entried \((0,1)\)-matrices.
MSC:
| 15A30 | Algebraic systems of matrices |
References:
| [1] | Rosenthal, D., Words containing a basis for the algebra of all matrices, Linear Algebra Appl., 436, 2615-2617, (2012) · Zbl 1236.15041 · doi:10.1016/j.laa.2011.08.048 |
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