Name
Title | ||
|---|---|---|
Relation between the T-congruence Sylvester equation and the generalized Sylvester equation |
Abstract | ||
|---|---|---|
The T-congruence Sylvester equation is the matrix equation AX+XTB=C, where A∈Rm×n, B∈Rn×m, and C∈Rm×m are given, and X∈Rn×m is to be determined. Recently, Oozawa et al. discovered a transformation that the matrix equation is equivalent to one of the well-studied matrix equations (the Lyapunov equation); however, the condition of the transformation seems to be too limited because matrices A and B are assumed to be square matrices (m=n). In this paper, two transformations are provided for rectangular matrices A and B. One of them is an extension of the result of Oozawa et al. for the case m≥n, and the other is a novel transformation for the case m≤n. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.aml.2019.04.007 | Applied Mathematics Letters |
Keywords | Field | DocType |
T-congruence Sylvester equation,Generalized Sylvester equation,The tensor product | Lyapunov equation,Sylvester equation,Matrix (mathematics),Mathematical analysis,Square matrix,Pure mathematics,Congruence (geometry),Mathematics | Journal |
Volume | ISSN | Citations |
96 | 0893-9659 | 0 |
PageRank | References | Authors |
0.34 | 3 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuki Satake | 1 | 0 | 0.34 |
| Masaya Oozawa | 2 | 0 | 0.34 |
| Tomohiro Sogabe | 3 | 154 | 20.86 |
| Yuto Miyatake | 4 | 17 | 4.40 |
| Tomoya Kemmochi | 5 | 0 | 0.34 |
| Shao-Liang Zhang | 6 | 92 | 19.06 |