Extension and generalization inequalities involving the Khatri-Rao product of several positive matrices

被引:11
作者
Al Zhour, Zeyad Abdel Aziz [1 ]
Kilicman, Adem
机构
[1] Univ Pertanian Malaysia, Dept Math, Serdang 43400, Selangor, Malaysia
[2] Univ Pertanian Malaysia, Inst Math Res, Serdang 43400, Selangor, Malaysia
关键词
Finite Number; Hadamard Product; Positive Matrice; Generalization Inequality;
D O I
10.1155/JIA/2006/80878
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Recently, there have been many authors, who established a number of inequalities involving Khatri-Rao and Hadamard products of two positive matrices. In this paper, the results are established in the following three ways. First, we find generalization of the inequalities involving Khatri-Rao product using results given by Liu ( 1999), Mond and Pecaric ( 1997), Cao et al. ( 2002), Chollet ( 1997), and Visick ( 2000). Second, we recover and develop some results of Visick. Third, the results are extended to the case of Khatri-Rao product of any finite number of matrices. These results lead to inequalities involving Hadamard product, as a special case.
引用
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页数:21
相关论文
共 10 条
[2]  
ALZHOUR ZA, 2005, P INT C MATH STAT TH, V1, P1
[3]  
Cao CG, 2002, ELECTRON J LINEAR AL, V9, P276
[4]   Some inequalities for principal submatrices [J].
Chollet, J .
AMERICAN MATHEMATICAL MONTHLY, 1997, 104 (07) :609-617
[5]   Matrix results on the Khatri-Rao and Tracy-Singh products [J].
Liu, SZ .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 289 (1-3) :267-277
[6]   Several inequalities involving Khatri-Rao products of positive semidefinite matrices [J].
Liu, SZ .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 354 (1-3) :175-186
[7]   Matrix inequalities for convex functions [J].
Mond, B ;
Pecaric, JE .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 209 (01) :147-153
[8]   A quantitative version of the observation that the Hadamard product is a principal submatrix of the Kronecker product [J].
Visick, G .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 304 (1-3) :45-68
[9]  
Zhang F., 1999, MATRIX THEORY BASIC
[10]  
Zhang X., 2002, APPL MATH E-NOTES, V2, P117