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The matrix S = [1+xiyj]i, j=1n, 0 < x1 < · · · < xn, 0 < y1 < · · · < yn, 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◦m = [(1+xiyj)m] for positive integers 1 ≤ m ≤ n-1. We also explore the total positivity of Hadamard powers of another important class of matrices called mean matrices. [ABSTRACT FROM AUTHOR]

The matrix S = [1+xiyj ]ni, j=1, 0 < x1 < · · · < xn, 0 < y1 < · · · < yn, 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◦m = [(1+xiyj)m] for positive integers 1 ≤ m ≤ n-1. We also explore the total positivity of Hadamard powers of another important class of matrices called mean matrices. [ABSTRACT FROM AUTHOR]