Drazin Inverse of Some Special Partitioned Matrices and Cubic Nilpontent Matrix
Zhuang Li-bin · Journal of Guiyang University · 2011
Campbell discussed the problem of expressing the generalized inverse of a partitioned block matrix[A B C 0],but the problem has not yet solved satisfactorily by scientists and researchers.Given the following partitioned block matrices [A AA* AA* 0],[AA* A A 0], where A is a cubic nilpontent matrix and A* is a transposed conjugate matrix of A,the expressions of Drazin inverses of those partitioned block matrices are given,by using formulas of Drazin inverses and Moore-Penrose inverses,and properties of cubic nilpontent matrix.