Compression and hadamard power inequalities

If , is an M-matrix, we show that the m-by-m matrix Â= the comparison matrix of (det Aij ) is also an M-matrix and that det Â≥ det A. This is analogous to known results for positive definite Hermitian matrices, but certain other compression analogies do not seem to carry over to M-matrices. In the case of H-matrices, determinantal compression preserves the class, but an analogous inequality does not hold. If A−(aij) and B=(bij) are M-matrices, we also give closure results and determinantal inequalities involving the comparison matrix of .