Related papers: Further Properties of Accretive Matrices
We study some (Hopf) algebraic properties of circulant matrices, inspired by the fact that the algebra of circulant $n\times n$ matrices is isomorphic to the group algebra of the cyclic group with $n$ elements. We introduce also a class of…
We discuss the use of matrices for providing sequences of rationals that approximate algebraic irrationalities. In particular, we study the regular representation of algebraic extensions, proving that ratios between two entries of the…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we…
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by…
Building on previous work that provided analytical solutions to generalised matrix eigenvalue problems arising from numerical discretisations, this paper develops exact eigenvalues and eigenvectors for a broader class of $n$-dimensional…
We give a natural definition for the transitivity of a matrix. Using an endomorphism d of a base ring R and a transitive nxn matrix over the center Z(R), we construct the subalgebra M_{n}(R,d,T) of the full nxn matrix algebra M_{n}(R)…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
It is proven that a certain class of positive maps in the matrix algebra $M_n$ consists of optimal maps, i.e. maps from which one cannot subtract any completely positive map without loosing positivity. This class provides a generalization…
In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…
Recently there has been several works estimating the number of $n\times n$ matrices with elements from some finite sets $\mathcal X$ of arithmetic interest and of a given determinant. Typically such results are compared with the trivial…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
The practically important classes of equal-input and of monotone Markov matrices are revisited, with special focus on embeddability, infinite divisibility, and mutual relations. Several uniqueness results for the classic Markov embedding…
We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…
We define geometric matrix midranges for positive definite Hermitian matrices and study the midrange problem from a number of perspectives. Special attention is given to the midrange of two positive definite matrices before considering the…
We describe a natural generalization of irreducibility in order lattices with arbitrary metrics. We analyse the special cases of valuation metrics and more general metrics for lattices. This article is mainly based on a part of the author's…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.