The Re-nonnegative definite solutions to the matrix equation

Qing Wen Wang; Chang Lan Yang

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 7-13
  • ISSN: 0010-2628

Abstract

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An complex matrix is called Re-nonnegative definite (Re-nnd) if the real part of is nonnegative for every complex -vector . 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 are presented.

How to cite

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Wang, Qing Wen, and Yang, Chang Lan. "The Re-nonnegative definite solutions to the matrix equation $AXB=C$." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 7-13. <http://eudml.org/doc/248253>.

@article{Wang1998,
abstract = {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.},
author = {Wang, Qing Wen, Yang, Chang Lan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Re-nonnegative define matrix; matrix equation; generalized singular value decomposition; Re-nonnegative definite matrix; matrix equation; generalized singular value decomposition},
language = {eng},
number = {1},
pages = {7-13},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The Re-nonnegative definite solutions to the matrix equation $AXB=C$},
url = {http://eudml.org/doc/248253},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Wang, Qing Wen
AU - Yang, Chang Lan
TI - The Re-nonnegative definite solutions to the matrix equation $AXB=C$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 7
EP - 13
AB - 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.
LA - eng
KW - Re-nonnegative define matrix; matrix equation; generalized singular value decomposition; Re-nonnegative definite matrix; matrix equation; generalized singular value decomposition
UR - http://eudml.org/doc/248253
ER -

References

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  8. Wang Q.W., Skewpositive semidefinite solutions to the quaternion matrix equation , Far East. J. Math. Sci., to appear. MR1432967
  9. Paige C.C., Saunders M.A., Towards a generalized singular value decomposition, SIAM J. Numer. Anal. 18 (1981), 398-405. (1981) Zbl0471.65018MR0615522
  10. Stewart G.W., Computing the CS-decomposition of a partitioned orthogonal matrix, Numer. Math. 40 (1982), 297-306. (1982) MR0695598

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