| Title:
|
The Re-nonnegative definite solutions to the matrix equation $AXB=C$ (English) |
| Author:
|
Wang, Qingwen |
| Author:
|
Yang, Changlan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
7-13 |
| . |
| Category:
|
math |
| . |
| Summary:
|
An $n\times n$ complex matrix $A$ is called Re-nonnegative definite (Re-nnd) if the real part of $x^{\ast } Ax$ is nonnegative for every complex $n$-vector $x$. In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation $AXB=C$ are presented. (English) |
| Keyword:
|
Re-nonnegative define matrix |
| Keyword:
|
matrix equation |
| Keyword:
|
generalized singular value decomposition |
| MSC:
|
15A24 |
| MSC:
|
15A57 |
| idZBL:
|
Zbl 0937.15008 |
| idMR:
|
MR1622312 |
| . |
| Date available:
|
2009-01-08T18:38:31Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118980 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Wang Q.W.: Skewpositive semidefinite solutions to the quaternion matrix equation $AXB=C$.Far East. J. Math. Sci., to appear. MR 1432967 |
| Reference:
|
[9] Paige C.C., Saunders M.A.: Towards a generalized singular value decomposition.SIAM J. Numer. Anal. 18 (1981), 398-405. Zbl 0471.65018, MR 0615522 |
| Reference:
|
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| . |
