DETERMINANTAL INEQUALITIES OF POSITIVE DEFINITE MATRICES

被引：6
|
作者：
Choi, Daeshik [1 ]
机构：
[1] So Illinois Univ, Edwardsville Dept Math & Stat, Box 1653, Edwardsville, IL 62026 USA
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2016年 / 19卷 / 01期
关键词：
Determinantal inequalities; Fischer's inequality; determinants of block matrices; positive definite matrices;
D O I：
10.7153/mia-19-12
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let A(i), i = 1, ..., m, be positive definite matrices with diagonal blocks A(i)((j)), 1 <= j <= k, where A(1)((j)), ..., A(m)((j)) are of the same size for each j. We prove the inequality det (Sigma(m)(i=1)A(i)(-1)) >= det(Sigma(m)(i=1)(A(i)((1)))(-1))center dot center dot center dot det(Sigma(m)(i=1)(A(i)((k)))(-1)) and more determinantal inequalities related to positive definite matrices.
引用
收藏
页码：167 / 172
页数：6
相关论文
共 50 条
  • [31] Inequalities for Kronecker products and Hadamard products of positive definite matrices
    Chansangiam, Pattrawut
    Hemchote, Patcharin
    Pantaragphong, Praiboon
    SCIENCEASIA, 2009, 35 (01): : 106 - 110
  • [32] Norm inequalities for positive definite matrices related to a question of Bourin
    Darweesh, Amer
    Hayajneh, Mostafa
    Hayajneh, Saja
    Kittaneh, Fuad
    LINEAR & MULTILINEAR ALGEBRA, 2023, 71 (12): : 1933 - 1947
  • [33] ON SYMMETRIC NORM INEQUALITIES AND POSITIVE DEFINITE BLOCK-MATRICES
    Mhanna, Antoine
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2018, 21 (01): : 133 - 138
  • [34] Nesbitt and Shapiro cyclic sum inequalities for positive definite matrices
    Projesh Nath Choudhury
    K. C. Sivakumar
    Advances in Operator Theory, 2022, 7
  • [35] DETERMINANTAL INEQUALITIES FOR BLOCK TRIANGULAR MATRICES
    Lin, Minghua
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2015, 18 (03): : 1079 - 1086
  • [36] Trace inequalities involving positive semi-definite block matrices
    Fu, Xiaohui
    Gumus, Mehmet
    LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (20): : 5987 - 5994
  • [37] MATRICES WITH POSITIVE DEFINITE HERMITIAN PART - INEQUALITIES AND LINEAR-SYSTEMS
    MATHIAS, R
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 162 : 770 - 775
  • [38] A simple proof of some inequalities for matrices with positive definite Hermitian part
    He, Gan-Tong
    PROCEEDINGS OF THE 14TH CONFERENCE OF INTERNATIONAL LINEAR ALGEBRA SOCIETY, 2007, : 63 - 65
  • [39] EXPONENTIAL CONVEXITY, POSITIVE SEMI-DEFINITE MATRICES AND FUNDAMENTAL INEQUALITIES
    Anwar, M.
    Jaksetic, J.
    Pecaric, J.
    Rehman, Atiq Ur
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2010, 4 (02): : 171 - 189
  • [40] ON THE ARITHMETIC-GEOMETRIC-HARMONIC-MEAN INEQUALITIES FOR POSITIVE DEFINITE MATRICES
    ANDO, T
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1983, 52-3 (JUL) : 31 - 37
12345