On a matrix result in comparison of linear experiments Original Research Article

A useful statistical relation between normal linear experiments image and image is reduced in [Stimagepniak, Statistics 30 (1998) 279–289] to the matrix conditions A′(V+AA′)−A−B′(W+BB′)−Bgreater-or-equal, slanted0 and r(V+AA′)−r(A)greater-or-equal, slantedr(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.