Equations \(ax = c\) and \(xb = d\) in rings and rings with involution with applications to Hilbert space operators (Q947645)
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: Equations \(ax = c\) and \(xb = d\) in rings and rings with involution with applications to Hilbert space operators |
scientific article; zbMATH DE number 5349150
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equations \(ax = c\) and \(xb = d\) in rings and rings with involution with applications to Hilbert space operators |
scientific article; zbMATH DE number 5349150 |
Statements
Equations \(ax = c\) and \(xb = d\) in rings and rings with involution with applications to Hilbert space operators (English)
0 references
6 October 2008
0 references
The authors review the equations \(ax = c\) and \(xb = d\) in the setting of associative rings with or without involution. The study of common solutions of the equations above in the framework of matrices dates back to the early 20th century; see \textit{F. Cecioni} [``Sopra alcune operazioni algebriche sulle matrici'' (Pisa Ann.\ 11) (1910; JFM 41.0193.02)]. The authors give necessary and sufficient conditions for the existence of the Hermitian, skew-Hermitian, reflexive, antireflexive, positive and real-positive solutions, and describe the general solutions in terms of the original elements or operators.
0 references
ring
0 references
ring with involution
0 references
equations in a ring
0 references
Hermitian solution
0 references
reflexive solution
0 references
matrix equations
0 references
operator equations
0 references
Hilbert space operators
0 references
positive solution
0 references
real-positive solution
0 references
0 references
