四元数体上Hermite矩阵的最小化问题

Minimization Problem for Hermitian Matrices over the Quaternion Field

该文建立了四元数矩阵对的标准相关分解(CCD-Q).借助CCD-Q,GSVD-Q和有限维内积空间中的投影定理,该文得到了基于四元数矩阵方程AXB=C的Hermite矩阵最小化问题解的表达式.

In this paper,the canonical correlation decomposition of quaternion matrices（CCDQ） is established.Based on the CCD-Q,GSVD-Q,and the projection theorem in the finite dimensional inner product space,the expression of minimization problem for Hermitian matrices associated with the quaternion matrix equation AXB=C is derived.