Quasi-Toeplitz row-equivalence conjecture

A quasi-Toeplitz matrix is a matrix obtained from a Toeplitz matrix by replacing some of its rows by zero rows. Two matrices are row equivalent when one can be obtained from the other by elementary row operations.

Quasi-Toeplitz row-equivalence conjecture. Every $n\times n$ matrix is row equivalent to a quasi-Toeplitz matrix.

If true, this would provide a systematic reduction of arbitrary matrices to a class that the paper identifies as particularly amenable to decomposition into Toeplitz factors. The paper does not provide a proof or a counterexample.