Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
473344 | Computers & Mathematics with Applications | 2008 | 7 Pages |
Abstract
Let R∈Cm×m and S∈Cn×n be nontrivial unitary involutions, i.e., RH=R=R−1≠ImRH=R=R−1≠Im and SH=S=S−1≠InSH=S=S−1≠In. We say that G∈Cm×n is a generalized reflexive matrix if RGS=GRGS=G. The set of all m×nm×n generalized reflexive matrices is denoted by GRCm×n. In this paper, a sufficient and necessary condition for the matrix equation AXB=D, where A∈Cp×m,B∈Cn×q and D∈Cp×q, to have a solution X∈GRCm×n is established, and if it exists, a representation of the solution set SXSX is given. An optimal approximation between a given matrix X̃∈Cm×n and the affine subspace SXSX is discussed, an explicit formula for the unique optimal approximation solution is presented, and a numerical example is provided.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Yongxin Yuan, Hua Dai,