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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Assume that X, partitioned into 2×2 block form, is a solution of the system of quaternion matrix equations A_1XB_1=C_1,A_2XB_2=C_2. We in this paper give the maximal and minimal ranks of the submatrices in X, and establish necessary and sufficient conditions for the submatrices to be zero, unique as well as independent. As applications, we consider the common inner inverse G, partitioned into 2×2 block form, of two quaternion matrices M and N. We present the formulas of the maximal and minimal ranks of the submatrices of G, and describe the properties of the submatrices of G as well. The findings of this paper generalize some known results in the literature.
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참고문헌 (16)
참고문헌 신청
A. B. Ozguler / 1991 / A common solution to a pair of linear matrix equations over a principle domain / Linear Algebra Appl 144 : 85 ~ 99
F. Uhlig / 1987 / On the matrix equation AX = B with applications to the generators of con- trollability matrix / Linear Algebra Appl 85 : 203 ~ 209
J. Van der Woude / 1987 / Almost noninteracting control by measurement feedback / Systems Control Lett 9 (1) : 7 ~ 16
M. Dehghan / 2008 / An iterative algorithm for solving a pair of matrix equa-tions AY B = E;CY D = F over generalized centro-symmetric matrices / Comput. Math. Appl 56 (12) :
Q. W. Wang / 1996 / The decomposition of pairwise matrices and matrix equations over an arbitrary skew field / Acta Math. Sinica 39 (3) : 396 ~ 403
F. Uhlig / 1987 / On the matrix equation AX = B with applications to the generators of con- trollability matrix / Linear Algebra Appl 85 : 203 ~ 209
J. Van der Woude / 1987 / Almost noninteracting control by measurement feedback / Systems Control Lett 9 (1) : 7 ~ 16
M. Dehghan / 2008 / An iterative algorithm for solving a pair of matrix equa-tions AY B = E;CY D = F over generalized centro-symmetric matrices / Comput. Math. Appl 56 (12) :
Q. W. Wang / 1996 / The decomposition of pairwise matrices and matrix equations over an arbitrary skew field / Acta Math. Sinica 39 (3) : 396 ~ 403
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