Inequalities involving Khatri-Rao products of Hermitian matrices Article Received: 09 November 2000 Revised: 25 July 2001 Abstract
Recently, several inequalities involving Khatri-Rao products of two four partitioned blocks positive definite real symmetry matrices are established by Liu in [Lin. Alg. Appl. 289(1999):267-277]. We extend these results in two ways. First, the results are extended to two any partitioned blocks Hermitian matrices. Second, necessary and sufficient conditions under which these inequalities become equalities are presented.
AMS Mathematics Subject Classification 15A45 15A69 Key words and phrases Matrix inequality Spectral decomposition Hadamard product Khatri-Rao product Tracy-Singh product Kronecker product
Partially supported by the Natural Science Foundation of Heilongjiang and the N. S. F. of Heilongjiang Education Committee.
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