Related papers: Developed Matrix inequalities via Positive Multili…
We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.
We present certain techniques to find completely positive maps between matrix algebras that take prescribed values on given data. To this aim we describe a semidefinite programming approach and another convex minimization method supported…
In this article, we define a matrix multinomial distribution. We prove some properties of the matrix multinomial distribution. We prove that the matrix Poisson distribution can be used as an approximation to the matrix multinomial…
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations…
We study $k$-positive linear maps on matrix algebras and address two problems, (i) characterizations of $k$-positivity and (ii) generation of non-decomposable $k$-positive maps. On the characterization side, we derive optimization-based…
There are four variants of passive, linear time-invariant systems, described by rational functions: Continuous or Discrete time, Positive or Bounded real. By introducing a quadratic matrix inequality formulation, we present a unifying…
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…
We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…
In the field of the Jacobian conjecture it is well-known after Druzkowski that from a polynomial "cubic-homogeneous" mapping we can build a higher-dimensional "cubic-linear" mapping and the other way round, so that one of them is invertible…
In this paper, we investigate set-valued maps of strongly and approximately Jensen convex and Jensen concave type. We present counterparts of the Bernstein--Doetsch Theorem with Tabor type error terms.
We consider certain matricial analogues of optimal mass transport of positive definite matrices of equal trace. The framework is motivated by the need to devise a suitable geometry for interpolating positive definite matrices in ways that…
An alternative characterization of Minkowski--Lyapunov functions is derived. The derived characterization enables a computationally efficient utilization of Minkowski--Lyapunov functions in arbitrary finite dimensions. Due to intrinsic…
In this paper, we give new singular value inequalities and determinant inequalities including the inverse of $A$, $B$ and $A+B$ for sector matrices. We also give the matrix inequalities for sector matrices with a positive multilinear map.…
This paper investigates Positivstellens\"atze for polynomial matrices subject to universally quantified polynomial matrix inequality constraints. We first establish a matrix-valued Positivstellensatz under the Archimedean condition,…
A unified matrix-vector representation is developed of such solution concepts as the core, the uncovered, the uncaptured, the minimal weakly stable, the minimal undominated, the minimal dominant and the untrapped sets. We also propose…
We study connections between linear equations over various semigroups and recursively enumerable sets of positive integers. We give variants of the universal Diophantine representation of recursively enumerable sets of positive integers…
In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
Multivalued projections are applied to the study of weighted least squares solutions of linear relations equations (or inclusions) and some of its applications. To this end a matrix representation of multivalued projections with respect to…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
Characterizing simultaneously diagonalizable (SD) matrices has been receiving considerable attention in the recent decades due to its wide applications and its role in matrix analysis. However, the notion of SD matrices is arguably still…