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초록· 키워드
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A matrix P∈C^(n×n) is called a
generalized reflection matrix if P^(*) and P^(2)=I. An
n×n complex matrix A is said to be a reflexive
(anti-reflexive) matrix with respect to the generalized reflection
matrix P if A=PAP (A=-PAP). It is well-known that the reflexive and anti-reflexive matrices with respect to the generalized
reflection matrix P have many special properties and widely used in engineering and scientific computations.
In this paper, we give new necessary and sufficient conditions for the existence of the reflexive (anti-reflexive) solutions
to the linear matrix equation AXB+CYD=E and derive representation
of the general reflexive (anti-reflexive) solutions to this matrix equation. By using the obtained results, we investigate the reflexive (anti-reflexive) solutions of some special cases of this matrix equation.
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참고문헌 (26)
참고문헌 신청
D. S. Cvetkovi´c-Ili´c / 2006 / The reflexive solutions of the matrix equation AXB = C / Comput. Math. Appl 51 (6) : 897 ~ 902
D. S. Cvetkovi´c-Ili´c / 2008 / Re-nnd solutions of the matrix equation AXB = C / J. Aust. Math. Soc 84 (1) : 63 ~ 72
Dragana S. Cvetkovic-Ilic / 2008 / The solutions of some operator equations / 대한수학회지 45 (5) : 1417 ~ 1425
F. Ding / 2005 / Gradient based iterative algorithms for solving a class of matrix equations / IEEE Trans. Automat. Control 50 (8) : 1216 ~ 1221
F. Ding / 2005 / Hierarchical gradient-based identification of multivariable discrete-time systems / Automatica J. IFAC 41 (2) : 315 ~ 325
D. S. Cvetkovi´c-Ili´c / 2008 / Re-nnd solutions of the matrix equation AXB = C / J. Aust. Math. Soc 84 (1) : 63 ~ 72
Dragana S. Cvetkovic-Ilic / 2008 / The solutions of some operator equations / 대한수학회지 45 (5) : 1417 ~ 1425
F. Ding / 2005 / Gradient based iterative algorithms for solving a class of matrix equations / IEEE Trans. Automat. Control 50 (8) : 1216 ~ 1221
F. Ding / 2005 / Hierarchical gradient-based identification of multivariable discrete-time systems / Automatica J. IFAC 41 (2) : 315 ~ 325
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