Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the ex...Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the extreme ranks of the real matrices. As applications, we establish necessary and sufficient conditions for some special least-squares g-inverse and minimum norm g-inverse.展开更多
By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in g-inverse and reflexive inner inverse of 2× 2 partitioned matrices, and prove a conjecture in [Yiju Wan...By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in g-inverse and reflexive inner inverse of 2× 2 partitioned matrices, and prove a conjecture in [Yiju Wang, SIAM J. Matrix Anal. Appl., 19（2）, 407-415（1998）].展开更多
By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general sol...By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general solution or unique solution.展开更多
In this paper we compute Karmarkar's projections quickly using MoorePenrose g-inverse and matrix factorization. So the computation work of (ATD2A)-1is decreased.
文摘Through the real representations of quaternion matrices and matrix rank method, we give the expression of the real ma-trices in least-squares g-inverse and minimum norm g-inverse. From these formulas, we derive the extreme ranks of the real matrices. As applications, we establish necessary and sufficient conditions for some special least-squares g-inverse and minimum norm g-inverse.
基金the National Natural Science Foundation of China,Grant No.10371044
文摘By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in g-inverse and reflexive inner inverse of 2× 2 partitioned matrices, and prove a conjecture in [Yiju Wang, SIAM J. Matrix Anal. Appl., 19（2）, 407-415（1998）].
基金the NSF of Hunan Province and the Science and Technology Development Foundation of Xiangtan Polytechnic University
文摘By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general solution or unique solution.
文摘In this paper we compute Karmarkar's projections quickly using MoorePenrose g-inverse and matrix factorization. So the computation work of (ATD2A)-1is decreased.
