Boolean-rank-preserving operators and Boolean-rank-1 spaces (Q791676)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Boolean-rank-preserving operators and Boolean-rank-1 spaces |
scientific article; zbMATH DE number 3851390
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boolean-rank-preserving operators and Boolean-rank-1 spaces |
scientific article; zbMATH DE number 3851390 |
Statements
Boolean-rank-preserving operators and Boolean-rank-1 spaces (English)
0 references
1984
0 references
The authors prove that a Boolean linear operator from the set of \(n\times m\) Boolean matrices to itself \((m,n>1)\) preserves Boolean rank iff if preserves ranks 1, 2 iff it has the form UAV or \(UA^ tV\) for U, V permutation matrices. They also find the maximum cardinality and dimension of rank 1 subspaces of \(n\times m\) Boolean matrices.
0 references
Boolean linear operator
0 references
Boolean matrices
0 references
Boolean rank
0 references
