Given a diagonal matrix which is supposed to have no non-zero entry in the diagonal after the first one (if any) the function returns the diagonal (sub-)matrix without the columns and the row corresponding to the zero-entries in the diagonal (if any).
a diagonal matrix which must satisfy the following property: in the diagonal, every element after a zero is a zero.
a diagonal matrix without zeros in the diagonal, composed by the first rows and columns of the original matrix with non zeros in the diagonal (which are also the only ones)
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