A LINEAR ALGEBRA PROOF THAT THE INVERSE OF A STRICTLY ULTRAMETRIC MATRIX IS A STRICTLY DIAGONALLY DOMINANT STIELTJES MATRIX

It is well known that every n x n Stieltjes matrix has an inverse that is an n x n nonsingular symmetric matrix with nonnegative entries, an d it is also easily seen that the converse of this statement fails in general to be true for n > 2. In the preceding paper by Martinez, Mich on, and San Martin [SIAM J. Matrix Anal. Appl., 15 (1994), pp. 98-106] , such a converse result is in fact shown to be true for the new class of strictly ultrametric matrices. A simpler proof of this basic resul t is given here, using more familiar tools from linear algebra.