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In this paper, we mainly consider the determinantal representations of the unique solution and the general solution to the restricted system of quaternion matrix equations \[ \left\{ \begin{array} [c]{c} A_{1}X=C_{1}\\ XB_{2}=C_{2}, \end{array} \right. \mathcal{R}_{r}\left( X\right) \subseteq T_{1},\text{ } \mathcal{N}_{r}\left( X\right) \supseteq S_{1}, \] respectively. As an application, we show the determinantal representations of the general solution to the restricted quaternion matrix equation \[ AX+YB=E,\text{ }\mathcal{R}_{r}\left( X\right) \subseteq T_{1},\text{ }\mathcal{N}_{r}\left( X\right) \supseteq S_{1},\text{ }\mathcal{R} _{l}\left( Y\right) \subseteq T_{2},\text{ }\mathcal{N}_{l}\left( Y\right) \supseteq S_{2}. \] The findings of this paper extend some known results in the literature.
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참고문헌 (47)
참고문헌 신청
S. L. Adler / 1995 / Quaternionic Quantum Mechanics and Quantum Fields, International Series of Monographs on Physics, 88 / The Clarendon Press, Oxford University Press
H. Aslaksen / 1996 / Quaternionic determinants / Math. Intelligencer 18(3):57~65
Z. Bai / 2016 / Monotone iterative method for a class of fractional differential equations / Electronic Journal of Differential Equations 2016:1~8
A. Ben-Israel / 1982 / A Cramer rule for least-norm solutions of consistent linear equations / Linear Algebra Appl. 43:223~226
J. Cai / 2007 / On determinantal representation for the generalized inverse $A^{(2)}_{T,S}$ and its applications / Numer. Linear Algebra Appl. 14(3):169~182
H. Aslaksen / 1996 / Quaternionic determinants / Math. Intelligencer 18(3):57~65
Z. Bai / 2016 / Monotone iterative method for a class of fractional differential equations / Electronic Journal of Differential Equations 2016:1~8
A. Ben-Israel / 1982 / A Cramer rule for least-norm solutions of consistent linear equations / Linear Algebra Appl. 43:223~226
J. Cai / 2007 / On determinantal representation for the generalized inverse
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