Displacement structure of weighted pseudoinverses

摘要

Estimates for the rank of AMN†V−UAMN† and more general displacement of AMN† are presented, where AMN† is the weighted pseudoinverse of a matrix A. The results are applied to the close-to-Toeplitz, close-to-Vandermonde and close-to-Cauchy matrices. We extend the results due to Heinig and Hellinger in 1994.