Further inequalities involving the Khatri-Rao product
Inequalities involving Khatri-Rao and Tracy-Singh matrix products, which are extension of the Hadamard and Kronecker products to the case of partitioned matrices, respectively, are studied. Results, previously presented by \textit{G. P. H. Styan} [Linear Algebra Appl. 6, 217--240 (1973; Zbl 0255.15002)] on companion inequalities involving the Hadamard product using statistical reasoning in the context of multivariety analysis, are extended. New results including companion inequalities are established and the conditions for such inequalities to become equalities are given. Especially, new results based on the Schur complement method are presented in the case of non-singular Hermitian matrices where no positive definite matrices are required. In the positive definite matrix case, the Kantorovich-type inequalities are established.
scientific article; zbMATH DE number 5552968