  Using the language of Riordan arrays, we look at two related iterative
processes on matrices and determine which matrices are invariant under these
processes. In a special case, the invariant sequences that arise are
conjectured to have Hankel transforms that obey Somos-4 recurrences. A notion
of eigentriangle for a number triangle emerges and examples are given,
including a construction of the Takeuchi numbers.
