New results on the W-weighted Drazin inverse
M. Nikuie, Muhammad Zaini Ahmad · AIP conference proceedings · 2014
The dimension of largest Jordan block corresponding to the zero eigenvalue of A is called the index of matrix A and is denoted by ind(A). Let A∈Cm×n, W∈Cn×m. Then A has the unique W-weighted Drazin inverse, denoted by AD,W, which satisfies AWX = XWA, XWAWX = X, (AW)k+1XW = (AW)k, where ind(AW) = k . The W-weighted Drazin inverse in solving the linear system WAWx = b has been used. So far the effect of the generalized inverses such as pseudoinverse, Drazin inverse and {1} - inverse in solving fuzzy linear systems is investigated. In this paper some new results on the W-weighted Drazin inverse are given. This results in solving singular fuzzy linear system, constrained linear systems and etc, would be applied