Related papers: Choi matrices revisited
We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del logics to formalize paraconsistent fuzzy reasoning. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product…
This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a…
We present necessary and sufficient conditions for an n\times n complex matrix B to be unitarily similar to a fixed unicellular (i.e., indecomposable by similarity) n\times n complex matrix A
A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative…
In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.
Mueller and Jones matrices have been thoroughly studied as mathematical tools to describe the manipulation of the polarization state of classical light. In particular, the most general physical transformation on the polarization state has…
In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras.
A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related…
Given two linear transformations, with representing matrices $A$ and $B$ with respect to some bases, it is not clear, in general, whether the Tracy-Singh product of the matrices $A$ and $B$ corresponds to a particular operation on the…
When a matrix A with n columns is known to be well approximated by a linear combination of basis matrices B_1,..., B_p, we can apply A to a random vector and solve a linear system to recover this linear combination. The same technique can…
Bochner's theorem characterizes positive definite functions on groups through the positivity of their Fourier transforms and plays a fundamental role in Harmonic analysis. While Bochner-type results are known for certain classes of…
Let $a,b$ be elements in a unital C$^*$-algebra with $0\leq a,b\leq 1$. The element $a$ is absolutely compatible with $b$ if $$\vert a - b \vert + \vert 1 - a - b \vert = 1.$$ In this note we find some technical characterizations of…
A new connection between two different necessary conditions for a polymatroid to be linearly representable is presented. Specifically, we prove that the existence of a tensor product with the uniform matroid of rank two on three elements…
Chen has recently shown how the response matrix of a two-phase composite can be written as linear combinations of products of the component matrices. We elaborate on Chen's expansions by deriving them in a different way, which a. shows them…
To each symmetrizable Cartan matrix, we associate a finite free EI category. We prove that the corresponding category algebra is isomorphic to the algebra defined in [C. Geiss, B. Leclerc, and J. Schr\"{o}er, Quivers with relations for…
We study pairs $(A,B)$ of square matrices that are in additive (resp. multiplicative) finite free position, that is, the characteristic polynomial $\chi_{A+B}(x)$ (resp. $\chi_{AB}(x)$) equals the additive finite free convolution…
The aim of this paper is to introduce the notion of (noncommutative) transposed Poisson conformal algebras, which serve as the conformal analogues of transposed Poisson algebras and admit a rich class of identities. We show that the tensor…
We give necessary and sufficient conditions under which a density matrix acting on a two-fold tensor product space is separable. Our conditions are given in terms of quantum conditional information transmission.
Let $M_n$ denote the algebra of $n \times n$ complex matrices and let $\mathcal{A}\subseteq M_n$ be an arbitrary structural matrix algebra, i.e. a subalgebra of $M_n$ that contains all diagonal matrices. We consider injective maps $\phi :…
We determine the structure of linear maps on complex (real) square matrices sending unitary (orthogonal) matrices to multiples of unitary (orthogonal) matrices. The result is used to determine the linear preservers of matrix pairs…