The integer solutions of linear unilateral and bilateral matrix equations over quadratic rings (Q2812887)
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: Integer Solutions of Matrix Linear Unilateral and Bilateral Equations over Quadratic Rings |
scientific article; zbMATH DE number 6593018
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The integer solutions of linear unilateral and bilateral matrix equations over quadratic rings |
scientific article; zbMATH DE number 6593018 |
Statements
13 June 2016
0 references
integer solutions
0 references
quadratic rings
0 references
linear matrix equations
0 references
0 references
0 references
The integer solutions of linear unilateral and bilateral matrix equations over quadratic rings (English)
0 references
For the linear matrix equations \(AX+BY=C\) and \(AX+YB=C\) over the quadratic rings \(\mathbb Z[\sqrt{k}]\), necessary and sufficient conditions are established for the existence of integer solutions, i.e. the solutions \(X\) and \(Y\) over the ring of integers \(\mathbb Z\). A uniqueness criterion for the integer solutions of these equations is given and a method of their construction is presented.
0 references
