Results 71 to 80 of about 597 (98)

Hölder type inequalities for matrices

, 1998
We discuss Holder type inequalites involving (Ap + Bp)1/p for positive semi-definite matrices A , B . Matrix or trace inequalities of Holder type as well as weak majorizations of similar type are obtained.
T. Andô, F. Hiai
semanticscholar   +1 more source

Further developments of Furuta inequality of indefinite type

, 2010
A selfadjoint involutive matrix J endows Cn with an indefinite inner product [·, ·] given by [x,y] := 〈Jx,y〉 , x,y ∈ Cn. We study matrix inequalities for J -selfadjoint matrices with nonnegative eigenvalues.
N. Bebiano, R. Lemos, J. Providência, G. Soares   +3 more
semanticscholar   +1 more source

A generalization of a trace inequality for positive definite matrices

, 2010
In this note we generalize the trace inequality derived by [1] to the case where the number of terms of the sum (denoted by K) is ...
Belmega, E. V., Jungers, M., Lasaulce, S.   +2 more
core   +2 more sources

Monotonicity for entrywise functions of matrices [PDF]

arXiv, 2007
We characterize real functions $f$ on an interval $(-\alpha,\alpha)$ for which the entrywise matrix function $[a_{ij}] \mapsto [f(a_{ij})]$ is positive, monotone and convex, respectively, in the positive semidefiniteness order. Fractional power functions are exemplified and related weak majorizations are shown.
arxiv  

Brascamp-Lieb Inequalities for Non-Commutative Integration [PDF]

Documenta Mathematica, vol. 13, (2008) pages 553-584, 2008
We formulate a non-commutative analog of the Brascamp-Lieb inequality, and prove it in several concrete settings.
arxiv  

The Resolvent Average for Positive Semidefinite Matrices [PDF]

arXiv, 2009
We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean.
arxiv  

Refinements of the trace inequality of Belmega, Lasaulce and Debbah [PDF]

Aust. J. Math. Anal. Appl., 7 (2010) Art. 23, 2009
In this short paper, we show a certain matrix trace inequality and then give a refinement of the trace inequality proven by Belmega, Lasaulce and Debbah. In addition, we give an another improvement of their trace inequality.
arxiv  

Impressions of convexity - An illustration for commutator bounds [PDF]

Lin. Alg. Appl. 433(11-12), 1726-1759 (2010), 2010
We determine the sharpest constant $C_{p,q,r}$ such that for all complex matrices $X$ and $Y$, and for Schatten $p$-, $q$- and $r$-norms the inequality $$ \|XY-YX\|_p\leq C_{p,q,r}\|X\|_q\|Y\|_r $$ is valid. The main theoretical tool in our investigations is complex interpolation theory.
arxiv  

Loewner matrices of matrix convex and monotone functions [PDF]

arXiv, 2010
The matrix convexity and the matrix monotony of a real $C^1$ function $f$ on $(0,\infty)$ are characterized in terms of the conditional negative or positive definiteness of the Loewner matrices associated with $f$, $tf(t)$, and $t^2f(t)$. Similar characterizations are also obtained for matrix monotone functions on a finite interval $(a,b)$.
arxiv  

A survey on the DDVV-type inequalities [PDF]

arXiv
In this paper, we give a survey on the history and recent developments on the DDVV-type inequalities.
arxiv