### HERIMITIAN SOLUTIONS TO THE EQUATION AXA* + BYB* = C, FOR HILBERT SPACE OPERATORS

**DOI Number**

**First page**

**Last page**

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

bibitem{chang} {sc X. W. Chang {rm and} J. Wang}: textit{The symmetric solutions of the matrix equations $AX + YA = C$, $AXA^{T} + BYB^{T} = C$ and $(A^{T}XA, B^{T}XB) = (C, D)$}. Linear Algebra and Appl. {bf179} (1993), 171--189.

bibitem{dajic1} {sc A. Daji$ acute{c} $}: textit{Common solution of linear equations in ring, with application}. Electonic Journal of Linear Algebra, {bf30} (2015), 66--79.

bibitem{dajic2} {sc A. Daji'{c} {rm and} J. J. Koliha}: textit{Positive solution to the equation $AX=C$ and $XB=D$ for hilbert space operators}. J. Math. Anal. Appl. {bf333} (2007), 567--576.

bibitem{dajic3} {sc A. Daji$ acute{c} $ {rm and} J. J. Koliha}: textit{ Equations $ ax=c $ and $ xb=d $ in rings and rings with involution with applications to Hilbert space operators}. Linear Algebra and its Appl. {bf429} (2008), 1779--1809.

bibitem{deng} {sc Y. Deng {rm and} X. Hu}: textit{On solutions of matrix equation $AXA^{T} + BYB^{T} = C$}. Journal of Computational Math. {bf23} (2005), 17--26.

bibitem{farid} {sc F. O. Farid, M. S. Moslehian, et al.}: textit{On the Hermitian solutions to a system of adjointable operator equations}. Linear Algebra and its Appl. {bf437} (2012), 1854--1891.

bibitem{fillmore1} {sc P. A. Fillmore {rm and} J. P. Williams}: textit{On operator ranges}. Advances in Math. {bf7} (1971), 244--281.

bibitem{grob} {sc J. Gro$ss$}: textit{A note on the general Hermitian solution to $AXA^{*}=B$}. Bull. Malaysian Math. Soc. (Second Series), {bf21} (1998), 57--62.

bibitem{he1} {sc Z. H. He}: textit{Some new results on a system of sylvester-type quaternion matrix equations}. Linear and Multilinear Algebra, DOI: 10.1080/03081087.2019.1704213.

bibitem{he2} {sc Z. H. He, M. Wang {rm and} X. Liu}; textit{On the general solutions to some systems of quternion matrix equations}. RACSAM (2020), 114:95.

bibitem{he3} {sc Z. H. He}: textit{Some quaternion matrix equations involving $phi$-Hermicity}. Filomat, {bf33} (2019), 5097--5112.

bibitem{he4} {sc Z. H. He}: textit{A system of coupled quaternion matrix equations with seven unknowns and its applications}. Adv Appl Clifford Algebras, (2019), 29:38.

bibitem{khatri} {sc C. G. Khatri {rm and} S. K. Mitra}: textit{Hermitian and nonnegative definite solution of linear matrix equations}. SIAM J. Appl. Math. {bf31(4)} (1976), 579--585.

bibitem{li} {sc N. Li, J. Jiang {rm and} W. Wang}: textit{Hermitian solution to a quaternion matrix equation}. Applied Mechanics and materials, {bf50-51} (2011), 391--395.

bibitem{mitra1} {sc S. K. Mitra}: textit{Common solution to a pair of linear matrix equations $A_{1}XB_{1}=C_{1}$, $A_{2}XB_{2}=C_{2}$}. Mathematical Proceedings of the Cambridge Philosophical Society, {bf74} (1973), 213--216.

bibitem{mitra2} {sc S. K. Mitra}: textit{A pair of simultaneous linear matrix equations $A_{1}XB_{1}=C_{1}$, $A_{2}XB_{2}=C_{2}$ and a matrix programming problem}. Linear Algebra and its Appl. {bf131} (1990), 107--123.

bibitem{mousavi} {sc Z. Mousavi, R. Eskandari, et al.}: textit{Operator equations $AX+YB=C$ and $AXA^{*}+BYB^{*}=C$ in Hilbert $mathcal{C^{*}}$-Modules}. Linear Algebra and Its Appl. {bf 517} (2017), 85--98.

bibitem{navarra} {sc A. Navarra, P. L. Odell {rm and} D. M. Young}: textit{ A representation of the general common solution to the matrix equations $A_{1}XB_{1}=C_{1}$ and $A_{2}XB_{2}=C_{2}$ with applications}. Computers and Mathematics with Applications, {bf41} (2001), 929--935.

bibitem{ozgular1} {sc A. B. Ozguler {rm and} N. A. Akar}: textit{ A common solution to a pair of linear matrix equations over a principal domain}. Linear Algebra and its Appl. {bf144} (1991), 85--99.

bibitem{patricio} {sc P. Patr'{i}cio {rm and} R. Puystjens}: textit{About the von Neumann regularity of triangular block matrices}. Linear Algebra and its Appl. {bf332-334} (2001), 485-â502.

bibitem{phadke} {sc S. V. Phadke {rm and} N. K. Thakare}: textit{Generalized inverses and operator equations}. Linear Algebra and its Appl. {bf23} (1979), 191--199.

bibitem{mehdi} {sc M. Vosough {rm and} M. S. Moslehian}: textit{Solvability of the matrix inequality}. Linear and Multilinear Algebra, {bf 66(9)} (2017), 1799--1818.

bibitem{wang1} {sc Q. W. Wang}: textit{A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity}. Linear Algebra and its Appl. {bf384} (2004), 43--54.

bibitem{wang2} {sc Q. W. Wang {rm and} Z. H. He}: textit{Some matrix equations with applications}. Linear Multilinear Algebra, {bf60:11-12} (2012), 1327--1353.

bibitem{xu1} {sc Q. Xu}: textit{Common hermitian and positive solutions to the adjointable operator equations $AX=C$, $XB=D$}. Linear Algebra and its Appl. {bf429} (2008), 1--11.

bibitem{xu2} {sc Q. Xu, L. Sheng {rm and} Y. Gu}: textit{The solutions to some operator equations}. Linear Algebra and its Appl. {bf429} (2008), 1997--2024.

bibitem{xu3} {sc G. Xu, M. Wei {rm and} D. Zheng}: textit{On solutions of matrix equation $AXB + CYD = F$}. Linear Algebra and its Appl. {bf279} (1998), 93--109.

DOI: https://doi.org/10.22190/FUMI191108001B

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)