Recently, authors established a number of inequalities involving Khatri-Rao product of two positive matrices. Here, in this paper, the results are established in three ways. First, we find new Holder-type inequalities for Tracy-Singh and Khatri-Rao products of positive semi-definite matrices. Secondly, the results are extended to provide estimates of sums of the Khatri-Rao and Tracy-Singh products of any finite number of positive semi-definite matrices. Finally, the results lead to inequalities involving the Hadamard and Kronecker products, as a special case.
Key words: Tracy-Singh products, Khatri-Rao products, positive (semi) definite matrices, Holder inequalities
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