ON SOME CHARACTERIZATIONS OF PAIRWISE STAR ORTHOGONALITY USING RANK AND DAGGER ADDITIVITY AND SUBTRACTIVITY

The main results are that pairwise star orthogonality, A(i)A(j) = 0 a nd A(i)A(j) = 0 for all i not equal j, where A(l),..., A(k) are compl ex m X n matrices, is equivalent to (i) A(i) less than or equal toSig ma A(j) and to (ii) A(i) less than or equal to(rs) Sigma A(j) and Sigm a A(j)(dagger) = (Sigma A(j))(dagger), where i = l,...,k; here the sup erscript dagger denotes the Moore-Penrose inverse, while less than or equal to and less than or equal to(rs) denote, respectively, the star and rank-subtractivity (or minus) partial orderings. Five more charac terizations of the pairwise star orthogonality of k complex m X n matr ices are also presented. Our characterizations extend earlier results by Hartwig and Styan (1986) for k = 2.