Compatible preorders and linear operators on \({\mathbb{R}}^ n\) (Q802700)
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: Compatible preorders and linear operators on \({\mathbb{R}}^ n\) |
scientific article; zbMATH DE number 4198209
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Compatible preorders and linear operators on \({\mathbb{R}}^ n\) |
scientific article; zbMATH DE number 4198209 |
Statements
Compatible preorders and linear operators on \({\mathbb{R}}^ n\) (English)
0 references
1991
0 references
The authors characterize preorders (quasiorders, reflexive transitive binary relations) $R$-compatible with the vector space structure on \(R^ n\) in the sense that, if \(xRy\), \(zRw\), then \((x+z)R(y+w)\) and \((cx)R(cy)\), $c$ positive, and studies representations as intersections of total orders of the same type.
0 references
linear operators
0 references
compatible preorder
0 references
ordered group
0 references
Szpilrajn theorem
0 references
preordered vector space
0 references
quasiorders
0 references
total orders
0 references
