The weighted Drazin invertibility of rectangular matrixs over an arbitrary ring are studied.Some equivalent conditions and Characterizations are given for existence of the weighted Drazin inverse of a rectangular matr...The weighted Drazin invertibility of rectangular matrixs over an arbitrary ring are studied.Some equivalent conditions and Characterizations are given for existence of the weighted Drazin inverse of a rectangular matrix over an arbitrary ring.Moreover,the weighted Drazin inverse of a rectangular matrices product PAQ can be characterized and computed.This generalizes results obtained for the Drazin inverse of such product of square matrices.The results also apply to morphisms in(additive)categories.展开更多
设A是含单位元e的Banach代数,a,b,c∈A,M_(c)=(a c o b)∈M_(2)(A).本文提出了 Banach代数中元素的左、右广义Drazin可逆的概念.定义集合σgD(a)={λ∈C:a - λe不是广义Drazin可逆的}为元素a的广义Drazin谱.证明了σgD(a)∪σgD(a)=σg...设A是含单位元e的Banach代数,a,b,c∈A,M_(c)=(a c o b)∈M_(2)(A).本文提出了 Banach代数中元素的左、右广义Drazin可逆的概念.定义集合σgD(a)={λ∈C:a - λe不是广义Drazin可逆的}为元素a的广义Drazin谱.证明了σgD(a)∪σgD(a)=σgD(M_(c))∪W_(g),其中 W_(g) 是σgD (M_(c))的某些洞且W_(g)■σgD(a)∩σgD(b),或者更精细地W_(g)■σrgD(a)∩σlgD(b).此外,还研究了 Banach代数中元素的广义Drazin谱的其他性质.展开更多
分块矩阵的广义逆不仅在数学理论上有广泛研究,而且在自动化、系统控制、概率统计、数学规划等领域有着广泛的实际应用背景,尤其是在最小二乘问题,病态线性、非线性问题,不适定问题,回归、分布估计、马尔可夫链等统计问题,随机规划问题...分块矩阵的广义逆不仅在数学理论上有广泛研究,而且在自动化、系统控制、概率统计、数学规划等领域有着广泛的实际应用背景,尤其是在最小二乘问题,病态线性、非线性问题,不适定问题,回归、分布估计、马尔可夫链等统计问题,随机规划问题,控制论和系统识别问题等研究中广义逆更是发挥着重要的作用.但求任意2×2分块矩阵的Drazin逆表达式是一个未解决的问题,因此给出了分块矩阵[EED EED E 0],[EED ED E 0],[ED EED E 0],[ED ED E 0]的Drazin逆表达式,其中E为复数域上的方阵,ED为E的Drazin逆.展开更多
文摘The weighted Drazin invertibility of rectangular matrixs over an arbitrary ring are studied.Some equivalent conditions and Characterizations are given for existence of the weighted Drazin inverse of a rectangular matrix over an arbitrary ring.Moreover,the weighted Drazin inverse of a rectangular matrices product PAQ can be characterized and computed.This generalizes results obtained for the Drazin inverse of such product of square matrices.The results also apply to morphisms in(additive)categories.
文摘分块矩阵的广义逆不仅在数学理论上有广泛研究,而且在自动化、系统控制、概率统计、数学规划等领域有着广泛的实际应用背景,尤其是在最小二乘问题,病态线性、非线性问题,不适定问题,回归、分布估计、马尔可夫链等统计问题,随机规划问题,控制论和系统识别问题等研究中广义逆更是发挥着重要的作用.但求任意2×2分块矩阵的Drazin逆表达式是一个未解决的问题,因此给出了分块矩阵[EED EED E 0],[EED ED E 0],[ED EED E 0],[ED ED E 0]的Drazin逆表达式,其中E为复数域上的方阵,ED为E的Drazin逆.
