would not be identifiable. Example 3.2. To illustrate the abstract concept of a set of matrices that is re- constructible from rows, we borrow an example from (Chang 1996). We say that a square matrix P is diagonal largest in column (DLC) if P ( j, j ) > P ( i, j ) for all i = j . The set of DLC matrices is reconstructible from rows. While DLC serves as a good means for conceptualising a set of matrices that is reconstructible from rows, it has also been shown to be useful as an empirical test for model identifiability (Kaehler et al. 2015). As remarked in Chang (1996), it is not the only set of matrices that is reconstructible from rows but might be a reasonable assumption. Unfortunately, as branch lengths increase, the assumption of DLC becomes less reasonable. Example 3.3. Under very weak assumptions, as branch length increases the transi- tion probability matrix on that branch must tend towards its stationary limit. That is, all its rows must tend towards equality. Rows that are closer to equality are in some sense less likely to satisfy DLC. To illustrate the point, is DLC . is not DLC . P =   $^{0}$$^{.}$$^{5}$ 0 . 3 0 . 2 0 . 1 0 . 4 0 . 5 0 . 1 0 . 1 0 . 8    P 2 =    0 . 3 0 . 29 0 . 41 0 . 14 0 . 24 0 . 62 0 . 14 0 . 15 0 . 71    However, it is an important observation that there is no way of permuting the rows of the second matrix in the above example so that it is DLC. We are therefore motivated to coin the following term. Definition 3.4. A set of matrices S ( M ) is sympathetic to a set of matrices M if 15