Related papers: Linear matrix maps for which positivity and comple…
We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…
A class of linear positive, trace preserving maps in $M_n$ is given in terms of affine maps in $\bBR^{n^2-1}$ which map the closed unit ball into itself.
We study the normal map for plane projective curves, i.e., the map associating to every regular point of the curve the normal line at the point in the dual space. We first observe that the normal map is always birational and then we use…
We prove that $i)$ if $\mathcal{A}$ is $\lambda $-accessible and it is axiomatizable in (finitary) coherent logic then $\lambda $-pure maps are strict monomorphisms and $ii)$ if there is a proper class of strongly compact cardinals and…
Following an idea of Choi, we obtain a decomposition theorem for k-positive linear maps from Mm to Mn, where 2<=k<min{m,n}. As a consequence, we give an affirmative answer to Kye's conjecture (also solved independently by Choi) that every…
We study the filtering of the perspective of a regular operator map of several variables through a completely positive linear map. By this method we are able to extend known operator inequalities of two variables to several variables; with…
The Leinster matrix corresponding to a finite category has entries counting the number of morphisms between objects. A first question is to know which positive integer matrices come from at least one finite category. Here, that question…
We survey the history of totally positive matrices and the generalization to Lie groups. We describe a reduction of a bilinear form to a canonical form (generalizing the case of symplectic nondegenerate forms) using ideas from total…
This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension…
In this paper, we show that a completely positive linear map is weakly nuclear if and only if its complexification is weakly nuclear. It is shown that a real $C^*$-algebra is exact if and only if its complexification is exact and similar…
A matrix is called totally positive if every minor of it is positive. Such matrices are well studied and have numerous applications in Mathematics and Computer Science. We study how many times the value of a minor can repeat in a totally…
Companion matrices of the second type are characterized by properties that involve bilinear maps.
In this paper we study the operator inequality \phi(X)\leq X and the operator equation \phi(X)= X, where \phi is a w^*-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one…
Positive maps which are not completely positive are used in quantum information theory as witnesses for convex sets of states, in particular as entanglement witnesses and more generally as witnesses for states having Schmidt number not…
Computing $p \rightarrow q$ norm for matrices is a classical problem in computational mathematics and power iteration is a well-known method for computing $p \rightarrow q $ norm for a matrix with nonnegative entries. Here we define an…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
We show that an operator valued $\alpha$-completely positive map on a group G is given by a unitary representation of G on a Krein space which satisfies some condition. Moreover, two unitary equivalent such unitary representations define…
A map between operator spaces is called completely coarse if the sequence of its amplifications is equi-coarse. We prove that all completely coarse maps must be $\mathbb R$-linear. On the opposite direction of this result, we introduce a…
Let M be an archimedean quadratic module of real t-by-t matrix polynomials in n variables, and let S be the set of all real n-tuples where each element of M is positive semidefinite. Our key finding is a natural bijection between the set of…
We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. The result covers both matrices over finite fields with independent non-zero entries and…