On a matrix result in comparison of linear experiments

AbstractA useful statistical relation between normal linear experiments N(Aβ,σV) and N(Bβ,σW) is reduced in [Stȩpniak, Statistics 30 (1998) 279–289] to the matrix conditions A′(V+AA′)−A−B′(W+BB′)−B⩾0 and r(V+AA′)−r(A)⩾r(W+BB′)−r(B). The aim of this note is to present a characterization of these conditions in terms of linear transformations. This characterization may be useful for matrix theory and practice