cartan decomposition

The exchangeable necessary and sufficient condition of square matrix product on domain has been investigated by using the standard form of the resemblance matrix and generalization Jordan disassociation.

利用相似矩阵标准形与约当分解 ,讨论了域上方阵乘积可交换的充要条件 ,并给出了特殊矩阵的乘积可交换阵的形

At the same time, the exchangeable necessary and sufficient condition of square matrix product on quaternion field has been investigated by using the standard form of the resemblance matrix and generalization Jordan disassociation.

给出了四元数的矩阵表示及四元数乘积可交换的充要条件 ,并利用相似矩阵标准形与广义约当分解 ,讨论了四元数体上方阵乘积可交换的充要条件 ,并给出了特殊矩阵的乘积可交换阵的形式 。

Using Jordan decomposition for matrixes, descriptor systems can be changed into normal systems.

运用矩阵约当分解,将一类广义系统化为正常系统,并利用已有的正常系统结果,给出一类广义最优Kalman滤波器,其算法简单,为递推算法,且避免了计算ARMA新息模型和白噪声估值器,便于实时应用。

For the sake of using the research of normal systems easily,descriptor systems are changed into normal systems by using Jordan decomposition of matrixes and their observability is hold on.

为了便于利用现有的正常系统研究结果,运用矩阵的约当分解,将一类广义系统化为正常系统,并保持其可观测性不变。

As one of applications,the Jordan decomposition theorem of a properly defined signed vector-valued measure is obtained,and the signed .

作为应用之一,在合理定义了广义矢值测度后,得到了约当分解定理,并且这种广义矢值测度就是一个模糊数值测度。