任意多个Hermitian矩阵的Khatri-Rao乘积的一些不等式

Some Inequalities Involving the Khatri-Rao Product of Finite Number of Hermitian Matrices

最近 S.Liu[2 ]和笔者 [4]得到了两个 Hermite矩阵的 Khatri- Rao乘积的一些不等式 .我们以两种方式来推广这些结果 .首先 ,将结论推广到任意有限个 Hermite矩阵的 Khatri- Rao乘积 ;其次 ,给出了相应不等式的等式成立的充分必要条件 .

Recently, several inequalities involving the Khatri Rao product of two Hermitian matrices are established by S. Liu in and by Z. Yang, X. Zhang & C. Cao in . We extend these results in two ways. First, the results are extended to the Khatri Rao product of any finite number of Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.