  The matrix $S = [1+x_i y_j]_{i,j=1}^{n}, 0<x_1<\cdots<x_n,\,
0<y_1<\cdots<y_n$, has gained importance lately due to its role in powers
preserving total nonnegativity. We give an explicit decomposition of $S$ in
terms of elementary bidiagonal matrices, which is analogous to the Neville
decomposition. We give a bidiagonal decomposition of $S^{\circ
m}=[(1+x_iy_j)^m]$ for positive integers $1\leq m \leq n-1$. We also explore
the total positivity of Hadamard powers of another important class of matrices
called mean matrices.
