Results 41 to 50 of about 597 (98)
Reduced relative quantum entropy [PDF]
arXiv, 2022 We introduce the notion of reduced relative quantum entropy and prove that it is convex. This result is then used to give a simplified proof of a theorem of Lieb and Seiringer.
arxiv
On the sum of powers of square matrices
Operators and Matrices, 2019 Given a 2×2 matrix A , we obtain the formula for sum of An , (n∈ Z) , using its trace and determinant only; this includes the negative powers in the case of a nonsingular matrix too. Here we mean by sum, the sum of all the entries of the matrix.
D. J. Karia, K. Patil, H. P. Singh
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Positive linear maps and eigenvalue estimates for nonnegative matrices [PDF]
arXiv, 2020 We show how positive unital linear maps can be used to obtain some bounds for the eigenvalues of nonnegative matrices.
arxiv
An extension of the Golden-Thompson theorem
, 2014 In this paper, we shall prove |treA+B|≤tr(|eA||eB|) for normal matrices A, B. In particular, treA+B≤tr(eAeB) if A, B are Hermitian matrices, yielding the Golden-Thompson inequality.MSC:15A16, 47A63, 15A45.
Hongyi Li, Di Zhao
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Inequalities for certain powers of several positive definite matrices
Mathematical Inequalities & Applications, 2019 Let Ai, i = 1, ...,m, and X be n×n matrices such that each Ai is positive definite with 0 < ai sn (Ai) and X is Hermitian. Then it is shown that ∣∣∣∣ ∣∣∣∣ ∣∣∣∣ ( m ∑ i=1 A am+1−i i ) X +X ( m ∑ i=1 Ai m+1−i ∣∣∣∣ ∣∣∣∣ ∣∣∣∣ m(1+ l2) |||X ||| , for every ...
Fadi Alrimawi
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Reversed determinantal inequalities for accretive-dissipative matrices
, 2012 A matrix A∈Mn(C) is said to be accretive-dissipative if, in its Toeplitz decomposition A = B+ iC , B = B∗ , C = C∗ , both matrices B and C are positive definite. Let A = [ A11 A12 A21 A22 ] be an accretive-dissipative matrix, k and l be the orders of A11
Minghua Lin
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Inequalities for certain powers of positive definite matrices
Mathematical Inequalities & Applications, 2019 Let A,B, and X be n× n matrices such that A,B are positive definite and X is Hermitian. If a and b are real numbers such that 0 < a sn (A) and 0 < b sn (B) , then it is shown, among other inequalities, that ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣AX +XBa ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ (1 ...
Fadi Alrimawi, O. Hirzallah, F. Kittaneh
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A note on the sensitivity analysis for the symplectic QR factorization
, 2017 In this note, the rigorous perturbation bounds for R factor of the implicit Bunch form of the symplectic QR factorization under normwise perturbation are derived by using the block matrix-vector equation approach, the technique of Lyapunov majorant ...
Hanyu Li, Peng Lv
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Some results on the partial orderings of block matrices
Journal of Inequalities and Applications, 2011 Some results relating to the block matrix partial orderings and the submatrix partial orderings are given. Special attention is paid to the star ordering of a sum of two matrices and the minus ordering of matrix product. Several equivalent conditions for
Liu Xifu, Yang Hu
doaj
A generalization of Maclaurin's inequalities and its applications
, 2005 The well-known Maclaurin’s inequalities are generalized as follows: If x and y are two positive n -tuples, and y and x/y are similarly ordered, then P n (x)/P [1] n (y) P n (x)/P n (y) · · · P n (x)/P n (y) · · · P n (x)/P n (y), where P n (a) is the k ...
J. Pečarić +3 more
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