Reverses and variations of Heinz inequality
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In this article, the reverse Heinz-type inequalities involving Hadamard product of the formin which is a unitarily invariant norm were established for positive definite matrices.Abstract:
Let be positive definite matrices. We present several reverse Heinz-type inequalities, in particularwhere is an arbitrary matrix, is Hilbert–Schmidt norm and . We also establish a Heinz-type inequality involving Hadamard product of the formin which and is a unitarily invariant norm.read more
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References
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Improved Young and Heinz inequalities for matrices
Fuad Kittaneh,Yousef Manasrah +1 more
TL;DR: In this paper, the authors give refinements of the classical Young inequality for positive real numbers and use these refinements to establish improved Young and Heinz inequalities for matrices, which are used in this paper.
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More matrix forms of the arithmetic-geometric mean inequality
Rajendra Bhatia,Chandler Davis +1 more
TL;DR: For arbitrary $n \times n$ matrices A, B, X, and for every unitarily invariant norm, it was shown in this paper that for any matrices B, A, X and B, it is possible to show that
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Reverse Young and Heinz inequalities for matrices
Fuad Kittaneh,Yousef Manasrah +1 more
TL;DR: This article gave reverses of the classical Young inequality for positive real numbers and used these reverses to establish reverse Young and Heinz inequalities for matrices, which were then used to establish the reverse Young inequalities for real numbers.
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Norm inequalities equivalent to heinz inequality
TL;DR: This article investigated several norm inequalities equivalent to the Heinz inequality and discussed the equivalence relations among these norm inequalities, and showed an elementary and simplified proof to the famous Heinz inequalities.