Results 61 to 70 of about 597 (98)

On the singular vectors of the generalized Lyapunov operator

, 2016
In this paper, we study the largest and the smallest singular vectors of the generalized Lyapunov operator. For real matrices A,B with order n , we prove that max‖X‖F =1 ‖AXBT + BXA‖F is achieved by a symmetric matrix for n 3 and give a counterexample ...
Sh. Chen, Yunbo Tian
semanticscholar   +1 more source

Note on Bounds for Eigenvalues using Traces [PDF]

arXiv, 2014
We show that various old and new bounds involving eigenvalues of a complex n x n matrix are immediate consequences of the inequalities involving variance of real and complex numbers.
arxiv  

Some inequalities for powers of positive definite matrices

, 2017
Mathematics subject classification (2010): 15A18, 15A42, 15A45, 15A60, 26C10. Keywords and phrases: Convex function, Hermitian matrix, positive semidefinite matrix, positive definite matrix, singular value, unitarily invariant norm.
Ata Abu s'ad, O. Hirzallah
semanticscholar   +1 more source

Precise estimates of bounds on relative operator entropies [PDF]

arXiv, 2014
Recently, Zou obtained the generalized results on the bounds for Tsallis relative operator entropy. In this short paper, we give precise bounds for Tsallis relative operator entropy. We also give precise bounds of relative operator entropy.
arxiv  

Schrödinger uncertainty relation with Wigner-Yanase skew information [PDF]

, 2010
We shall give a new Schr\"odinger type uncertainty relation for a quantity representing a quantum uncertainty, introduced by S.Luo in \cite{Luo1}. Our result improves the Heisenberg uncertainty relation shown in \cite{Luo1} for a mixed state.
arxiv   +1 more source

Generalization of Golden-Thompson type inequalities for normal matrices

, 2016
We survey some well-known matrix exponential formulae, with emphasis on logmajorization results, by using the compound matrix method. Mathematics subject classification (2010): 15A45, 15B48.
Xuhua Liu
semanticscholar   +1 more source

Some numerical characteristics of Sylvester and Hadamard matrices [PDF]

arXiv, 2015
We introduce numerical characteristics of Sylvester and Hadamard matrices and give their estimates and some of their applications.
arxiv  

An extension of Harnack type determinantal inequality [PDF]

arXiv, 2017
We revisit and comment on the Harnack type determinantal inequality for contractive matrices obtained by Tung in the nineteen sixtieth and give an extension of the inequality involving multiple positive semidefinite matrices.
arxiv  

Oppenheim's inequality and RKHS

, 2012
Applying norm inequalities for RKHSs corresponding to the product of reproducing kernels and using the minimal norm of the Nevanlinna interpolation, we give the basic background and essences of the quite famous fundamental inequalities, Oppenheim’s ...
A. Yamada
semanticscholar   +1 more source

A refined determinantal inequality for correlation matrices [PDF]

arXiv, 2019
Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.
arxiv