Power matrix means and related inequalities ∗

This survey paper contains recent results for power matrix means and related inequalities for convex functions, Hadamard product of matrices as well as some inequalities involving exponential function of matrices.

[1]  R. Subramanian,et al.  Inequalities between means of positive operators , 1978, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  G. Styan,et al.  Some further matrix extensions of the Cauchy-Schwarz and Kantorovich inequalities, with some statistical applications , 1996 .

[3]  Kunio Tanabe,et al.  Upper and lower bounds for the arithmetic-geometric-harmonic means of positive definite matrices , 1994 .

[4]  Ingram Olkin,et al.  Matrix versions of the Cauchy and Kantorovich inequalities , 1990 .

[5]  L. Ciach.  Around Jensen's inequality , 1994 .

[6]  Thomas Mathew,et al.  On the Matrix Convexity of the Moore-Penrose Inverse and Some Applications. , 1989 .

[7]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[8]  H. Wynn,et al.  G-majorization with applications to matrix orderings , 1985 .

[9]  B. Mond,et al.  On matrix convexity of the Moore-Penrose inverse , 1996 .

[10]  B. Mond,et al.  Matrix Inequalities for Convex Functions , 1997 .

[11]  D. S. Mitrinovic,et al.  Classical and New Inequalities in Analysis , 1992 .

[12]  Josip Pečarić,et al.  A matrix version of the Ky Fan Generalization of the Kantorovich inequality , 1994 .

[13]  K. Kedlaya.  Proof of a Mixed Arithmetic-Mean, Geomertic-Mean Inequality , 1994 .

[14]  Simo Puntanen,et al.  Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities , 1990 .

[15]  E. Beckenbach.  CONVEX FUNCTIONS , 2007 .

[16]  Charles R Johnson.  An inequality for matrices whose symmetric part is positive definite , 1973 .

[17]  P. Whittle.  A MULTIVARIATE GENERALIZATION OF TCHEBICHEV'S INEQUALITY , 1958 .

[18]  B. Mond,et al.  Reverse forms of a convex matrix inequality , 1995 .

[19]  S. Sherman,et al.  Monotone and convex operator functions , 1955 .

[20]  I. Olkin,et al.  A Multivariate Tchebycheff Inequality , 1958 .

[21]  Josip Pečarić,et al.  The arithmetic mean — the geometric mean and related matrix inequalities , 1997 .

[22]  C. Ballantine.  On the Hadamard product , 1968 .

[23]  R. Duffin,et al.  Series and parallel addition of matrices , 1969 .

[24]  C. Davis.  Notions generalizing convexity for functions defined on spaces of matrices , 1963 .

[25]  Shuangzhe Liu,et al.  Several Matrix Kantorovich-Type Inequalities , 1996 .

[26]  H. Neudecker,et al.  Asymptotics of Eigenvalues and Unit-Length Eigenvectors of Sample Variance and Correlation Matrices , 1993 .

[27]  M. H. Moore.  A Convex Matrix Function , 1973 .

[28]  Josip Pečarić,et al.  A MIXED ARITHMETIC-MEAN-HARMONIC-MEAN MATRIX INEQUALITY , 1996 .