Related papers: Some notes about matrices, 4
We introduce Hadamard matrices whose entries are quaternionic. We then go on to provide classification of quaternionic Hadamard matrices of circulant core of orders 2 through 5. We also introduce quaternionic Hadamard matrices of Butson…
This note revisits some majorization inequalities for eigenvalues, special attention is given to an elegant theorem of Hiroshima. An extension of the special case of Hiroshima's theorem is presented. Some discussion and open problems are…
We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~$2$ of lattices. %as considered in \cite{Ma1} and \cite{Ma2}. We also consider some related…
A new kind of diagrams is presented, showing the causal structure of bimetric interactions.
We characterize positive definiteness for some family of matrices. As an application we derive explicit value of the quadratic embedding constants of the path graphs.
This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.
In this (mostly expository) paper I want to share some observations prompted by a class of matrices whose determinants are Catalan numbers. Considering different methods of proof we obtain some generalizations and q-analogues and…
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
We study the time and space complexity of matrix permanents over rings and semirings.
The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals domains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a…
We give an overview of our effort to introduce (dual) semicanonical bases in the setting of symmetrizable Cartan matrices.
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
We extend Carleson's interpolation Theorem to sequences of matrices, by giving necessary and sufficient separation conditions for a sequence of matrices to be interpolating.
The aim of this note is to show that the properties like motivic decomposability, Chow theoretic decomposition of the diagonal etc. happens for the special member of a family if it happens for a general member of the family.
We briefly review the connection between the fuzzy field theories and matrix models and describe the main features of the models that appear. We summarize the different approaches to their analysis, some of the recent results and the…
To approximate a simple root of an equation we construct families of iterative maps of higher order of convergence. These maps are based on model functions which can be written as an inner product. The main family of maps discussed is…
We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising for this family of maps.
The work studies some Difference equations, which are connected with Mejer's function.