Results 21 to 30 of about 438 (51)
Maps on positive definite matrices preserving Bregman and Jensen divergences [PDF]
, 2015 In this paper we determine those bijective maps of the set of all positive definite $n\times n$ complex matrices which preserve a given Bregman divergence corresponding to a differentiable convex function that satisfies certain conditions.
Molnár, Lajos +2 more
core +2 more sources
A simple sufficient condition for complete positivity
, 2015 We use row sums and rank to give a sufficient condition on the diagonal entries of a doubly nonnegative matrix for it to be completely positive and its cp-rank equal to its rank. Mathematics subject classification (2010): 15A23, 15B48, 15B57.
W. So, Changqing Xu
semanticscholar +1 more source
Extensions of Three Matrix Inequalities to Semisimple Lie Groups
Special Matrices, 2014 We give extensions of inequalities of Araki-Lieb-Thirring, Audenaert, and Simon, in the context ofsemisimple Lie groups.
Liu Xuhua, Tam Tin-Yau
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The 123 theorem of Probability Theory and Copositive Matrices
Special Matrices, 2014 Alon and Yuster give for independent identically distributed real or vector valued random variablesX, Y combinatorially proved estimates of the form Prob(∥X − Y∥ ≤ b) ≤ c Prob(∥X − Y∥ ≤ a). We derivethese using copositive matrices instead.
Kovačec Alexander +2 more
doaj +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
Barabanov norms, Lipschitz continuity and monotonicity for the max algebraic joint spectral radius [PDF]
, 2017 We present several results describing the interplay between the max algebraic joint spectral radius (JSR) for compact sets of matrices and suitably defined matrix norms.
Ait-Rami +26 more
core +2 more sources
Polynomials with a sharp Cauchy bound and their zeros of maximal modulus
, 2015 The moduli of zeros of a complex polynomial are bounded by the positive zero of an associated auxiliary polynomial. The bound is due to Cauchy. This note describes polynomials with a sharp Cauchy bound and the location of peripheral zeros.
H. K. Wimmer
semanticscholar +1 more source
A note on matrices mapping a positive vector onto its element-wise inverse
, 2017 For any primitive matrix $M\in\mathbb{R}^{n\times n}$ with positive diagonal entries, we prove the existence and uniqueness of a positive vector $\mathbf{x}=(x_1,\dots,x_n)^t$ such that $M\mathbf{x}=(\frac{1}{x_1},\dots,\frac{1}{x_n})^t$.
Labbé, Sébastien
core +1 more source
Sufficient conditions for complete positivity
, 2011 Marcus and Minc gave sufficient conditions on the diagonal entries of a doubly nonnegative doubly stochastic n×n matrix A , that there is a doubly nonnegative doubly stochastic matrix C with A = C2 . In this event, A is completely positive.
Robert Reams
semanticscholar +1 more source
The integer cp-rank of 2 × 2 matrices
Special Matrices, 2019 We show the cp-rank of an integer doubly nonnegative 2 × 2 matrix does not exceed 11.
Laffey Thomas, Šmigoc Helena
doaj +1 more source