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Is there a name for matrices where the first non-zero entry of each row is the last non-zero entry of its column?

For example this matrix: $$\begin{pmatrix} 0 & \bf 1 & 0 & 1 \\ \bf 1 & 0 & 1 & 1 \\ 0 & 0 & 0 & \bf 1 \\ 0 & 0 & \bf 1 & 0 \\ \end{pmatrix}$$

Like row echelon form, they allow you to quickly determine the rank of a matrix, but I wasn't able to find how they are called (if they have a name).

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