Related papers: Improvements on some partial trace inequalities fo…
In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose…
A partial matrix is a matrix where only some of the entries are given. We determine the maximum rank of the symmetric completions of a symmetric partial matrix where only the diagonal blocks are given and the minimum rank and the maximum…
Denote by $\P_n$ the set of $n\times n$ positive definite matrices. Let $D = D_1\oplus \dots \oplus D_k$, where $D_1\in \P_{n_1}, \dots, D_k \in \P_{n_k}$ with $n_1+\cdots + n_k=n$. Partition $C\in \P_n$ according to $(n_1, \dots, n_k)$ so…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…
We prove an inequality that complements the famous Araki-Lieb-Thirring (ALT) inequality for positive matrices $A$ and $B$, by giving a lower bound on the quantity $\trace[A^r B^r A^r]^q$ in terms of $\trace[ABA]^{rq}$ for $0\le r\le 1$ and…
In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For…
Algebras generated by strictly positive matrices are described up to similarity, including the commutative, simple, and semisimple cases. We provide sufficient conditions for some block diagonal matrix algebras to be generated by a set of…
The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…
Hayashi's Pinching Inequality, which establishes a matrix inequality between a semidefinite matrix and a multiple of its "pinched" version via a projective measurement, has found many applications in quantum information theory and beyond.…
We propose halfspace depth concepts for scatter, concentration and shape matrices. For scatter matrices, our concept is similar to those from Chen, Gao and Ren (2017) and Zhang (2002). Rather than focusing, as in these earlier works, on…
We look for all linear isomorphisms from the mapping spaces onto the tensor products of matrices which send $k$-superpositive maps onto unnormalized bi-partite states of Schmidt numbers less than or equal to $k$. They also send $k$-positive…
The dual of a matrix ordered space has a natural matrix ordering that makes the dual space matrix ordered as well. The purpose of these notes is to give a condition that describes when the linear map taking a basis of the n by n matrices to…
A new criterion for A-stability of peer two-step methods is presented which is verifiable exactly in exact arithmetic by checking semi-definiteness of a certain test matrix. It depends on the existence of two positive definite weight…
We give a short proof of a recent result by Bernik, Mastnak, and Radjavi, stating that an irreducible group of complex matrices with nonnegative diagonal entries is diagonally similar to a group of nonnegative monomial matrices. We also…
In this paper, we establish the sharp critical and subcritical trace Trudinger-Moser and Adams inequalities on the half spaces and prove the existence of their extremals through the method based on the Fourier rearrangement, harmonic…
Using quantum maps we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy, in some systems, is demonstrated quantitatively. However, our study of the standard map cautions that this…
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…
We present a new trace estimator of the matrix whose explicit form is not given but its matrix multiplication to a vector is available. The form of the estimator is similar to the Hutchison stochastic trace estimator, but instead of the…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…