摘要
利用四元数矩阵对的广义奇异值分解,讨论四元数矩阵方程AXB=C具有反中心对称解的充要条件,得到解的具体表达式,并应用Frobenius范数酉不变性,在该方程的反中心对称解集合中导出与给定相同类型矩阵的最佳逼近解的表达式.
By using generalized singular value decomposition of quaternion matrices, the necessary and sufficient conditions of the quaternion matrix equation A×B = C having the anti-centro- symmetry solutions are discussed, and the specific expression of the solution is obtained. Meanwhile, by using unitary invariant property of Frobenius norm, the expression of the best approximation solution corresponding with given type of matrices are derived from the anti- centro-symmetry solutions set of this quaternion matrix equation.
出处
《广西科学院学报》
2008年第2期79-83,共5页
Journal of Guangxi Academy of Sciences
基金
广西自然科学基金项目(2008J32)
广西教育厅科研基金项目(2006J26)资助
