Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4631430 | Applied Mathematics and Computation | 2010 | 10 Pages |
Abstract
Suppose that p(X, Y) = A â BX â X(â)B(â) â CYC(â) and q(X, Y) = A â BX + X(â)B(â) â CYC(â) are quaternion matrix expressions, where A is persymmetric or perskew-symmetric. We in this paper derive the minimal rank formula of p(X, Y) with respect to pair of matrices X and Y = Y(â), and the minimal rank formula of q(X, Y) with respect to pair of matrices X and Y = âY(â). As applications, we establish some necessary and sufficient conditions for the existence of the general (persymmetric or perskew-symmetric) solutions to some well-known linear quaternion matrix equations. The expressions are also given for the corresponding general solutions of the matrix equations when the solvability conditions are satisfied. At the same time, some useful consequences are also developed.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Israr Ali Khan, Qing-Wen Wang, Guang-Jing Song,