Related papers: Choi matrices revisited
We continue the study of real polynomials acting entrywise on matrices of fixed dimension to preserve positive semidefiniteness, together with the related analysis of order properties of Schur polynomials. Previous work has shown that,…
Utilizing the notion of positive multilinear mappings, we give some matrix inequalities. In particular, Choi--Davis--Jensen and Kantorovich type inequalities including positive multilinear mappings are presented.
We give a simple direct proof of the Jamiolkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accesible for physicists than others found in the literature and provides a…
The cyclotomic matrix is commonly used to arrange cyclotomic numbers in a convenient format. A natural question is whether the structure of the matrix can reflect properties of these numbers. In this article, we examine cyclotomic numbers…
A square matrix $M$ with real entries is said to be algebraically positive (AP) if there exists a real polynomial $p$ such that all entries of the matrix $p(M)>0$. A square sign pattern matrix $S$ is said to allow algebraic positivity if…
We will introduce the notion of strong Morita equivalence for completely positive linear maps and study its basic properties. Also, we will discuss the relation between strong Morita equivalence for bounded $C^*$-bimodule linear maps and…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
Bhat characterizes the family of linear maps defined on $B(\mathcal{H})$ which preserve unitary conjugation. We generalize this idea and study the maps with a similar equivariance property on finite-dimensional matrix algebras. We show that…
A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…
Let K be an arbitrary field, and a,b,c,d be elements of K such that the polynomials t^2-at-b and t^2-ct-d are split in K[t]. Given a square matrix M with entries in K, we give necessary and sufficient conditions for the existence of two…
Multiplicativity of certain maximal p -> q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity (CP) is either augmented by, or replaced by, the requirement that…
A complete theory of the relationship between the minimal bases and indices of rational matrices and those of their strong linearizations is presented. Such theory is based on establishing first the relationships between the minimal bases…
It is widely believed that the Choi map generates an extremal ray in the cone $\mathcal P(M_3)$ of all positive linear maps between $C^*$-algebra $M_3$ of all $n\times n$ matrices over the complex field. But the only proven fact is that the…
We present a large class of indecomposable exposed positive linear maps between three dimensional matrix algebras. We also construct two qutrit separable states with lengths ten in the interior of their dual faces. With these examples, we…
Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process an equivalent to Witt's…
Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…
We prove that all injective maps on positive complex matrices which preserve order and shrink spectrum are implemented by unitary or antiunitary conjugations. We show by counterexamples that all assumptions are indispensable. The result…
In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
We study k Kadison Schwarz (k KS) mappings on matrix algebras and derive explicit conditions ensuring the k KS property for two classes of maps parameterized by a single k-positive map.