Displacement structure of weighted pseudoinverses

Estimates for the rank of A"M"N^@?V-UA"M"N^@? and more general displacement of A"M"N^@? are presented, where A"M"N^@? 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.

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