Ranks of least squares solutions of the matrix equation \(AXB=C\) (Q931764)
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: Ranks of least squares solutions of the matrix equation \(AXB=C\) |
scientific article; zbMATH DE number 5293423
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ranks of least squares solutions of the matrix equation \(AXB=C\) |
scientific article; zbMATH DE number 5293423 |
Statements
Ranks of least squares solutions of the matrix equation \(AXB=C\) (English)
0 references
26 June 2008
0 references
The author considers the complex matrix equation \(AXB=C\) and deals with the following two problems: (1) the maximal and minimal ranks of its least squares solution and (2) the maximal and minimal ranks of the real and of the imaginary parts of this least squares solution. He also gives necessary and sufficient conditions for the existence of a common least squares solution for two equations \(A_iXB_i=C_i\), \(i=1,2\).
0 references
solvability condition
0 references
least squares solution
0 references
maximal rank
0 references
minimal rank
0 references
common solution
0 references
generalized inverse
0 references
matrix rank method
0 references
complex matrix equation
0 references
0 references
0 references
0 references
