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Inequalities for the Singular Values of Hadamard Products
SIAM Journal on Matrix Analysis and Applications, 1997In their classical book ``Topics on matrix analysis'' (1991; Zbl 0729.15001), p. 334, \textit{R. A. Horn} and \textit{C. R. Johnson} gave an upper bound on the sum of the singular values of the Hadamard (Schur) product of two complex matrices in terms of the row and column lengths of one matrix and the singular values of the other matrix, and ...
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A generalization of hadamard's inequality
Linear and Multilinear Algebra, 1992If A = (ai,j ) is an n × n complex matrix then h(A) denotes the product of the diagonal entries of A, and if λ is a partition of n then [λ](A) is defined by where Sn denotes the symmetric group of degree n and {λ} is the ordinary irreducible character of Sn corresponding to λ. Let deg λ denote the degree of {λ}.
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An information-theoretic proof of Hadamard's inequality
IEEE Trans. Inf. Theory, 1983Summary: Hadamard's inequality follows immediately from inspection of both sides of the entropy inequality \(h(X_ 1,X_ 2,...,X_ n)\leq \sum h(X_ i)\), when \((X_ 1,X_ 2,...,X_ n)\) is multivariate normal.
Thomas M. Cover, Abbas A. El Gamal
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Some Inequalities Related to Hadamard Matrices
Functional Analysis and Its Applications, 2002The author defines a parameter \(\rho^{(n)}\) connected with an \(n\times n\) matrix \(A=(a_{ki})\) and a normalized basis \((\varphi_k)\) of a Banach space \(X\) by \[ \rho^{(n)} := \max_{1\leq m\leq 2^n} \Biggl\|\sum_{i=1}^{2^n} \sum_{k=1}^m a_{ki}\varphi_i\Biggr\|. \] Throughout it is assumed that \((\varphi_k)\) is subsymmetric with constant \(1\).
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On the Landau-Hadamard inequality
1992For any bounded real-valued function f defined on the whole real line ℝ or on the half-line (0, +∞), denote by ω(f) the oscillation of f, $$\omega \left( f \right) = \sup \;f - \inf \;f = \mathop {\sup }\limits_{x,y} \left( {f\left( x \right) - f\left( y \right)} \right),$$ and put, as usual, $${\left\| f \right\|_\infty } = \mathop {\sup ...
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On a Generalization of the Hermite-Hadamard Inequality II
2008Generalized form of Hermite-Hadamard inequality for (2n)-convex Lebesgue integrable functions are obtained through generalization of Taylor’s Formula.
Anwar, Matloob, Pečarić, Josip E.
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Hermite–Hadamard inequality for convex stochastic processes
Aequationes Mathematicae, 2011Dawid Kotrys
exaly
Hadamard's inequality and Trapezoid Rules for the Riemann–Stieltjes integral
Journal of Mathematical Analysis and Applications, 2008Peter R Mercer
exaly