四元数体上一类矩阵方程的极小范数最小二乘解
사원수체상일류구진방정적겁소범수최소이승해
The minimal norm and least square solution to a class of matrix equations in the quaternion field
  • 万方数据
    纯粹数学与应用数学 순수수학여응용수학
    PURE AND APPLIED MATHEMATICS
    2010年 2期 191-192,230 ,共3页

    邓勇%黄敬频%杜刚

    산용%황경빈%두강

    四元数体%矩阵方程%最小二乘解 四元數體%矩陣方程%最小二乘解
    사원수체%구진방정%최소이승해
    quaternion field%matrix equation%least square solution
    借助于四元数体上自共轭矩阵的奇异值分解,给出了四元数矩阵方程Ax+XB+CXD=F的极小范数最小二乘解.同时,在有解的条件下给出了Hermite最小二乘解及其通解的表达形式.
    차조우사원수체상자공액구진적기이치분해,급출료사원수구진방정Ax+XB+CXD=F적겁소범수최소이승해.동시,재유해적조건하급출료Hermite최소이승해급기통해적표체형식.
    By using the singular value decomposition of self-conjugate matrices in the quaternion field, we obtain the least square solutions with minimal norms to AX + XB + CXD = F. At the same time, we gave exact form of the least square solution of Hermite, if it has solutions.
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