Related papers: A study on Vandermonde-like polynomial matrices
We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gr\"obner bases. Each variety encodes a collection of matroids, whose flats…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
A three-parameter family of complex Hadamard matrices of order 6 is presented. It significantly extends the set of closed form complex Hadamard matrices of this order, and in particular contains all previously described one- and…
We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…
We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.
Balancedly splittable Hadamard matrices are introduced and studied. A connection is made to the Hadamard diagonalizable strongly regular graphs, maximal equiangular lines set, and unbiased Hadamard matrices. Several construction methods are…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…
We introduce two classes of homogeneous polynomials and show their role in constructing of integrable hierarchies for some integrable lattices.
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
Special polynomials associated with rational solutions of the second Painlev\'{e} equation and other members of its hierarchy are discussed. New approach, which allows one to construct each polynomial is presented. The structure of the…
We classify the matrices M which correspond to finite categories
We axiomatize and study the matrices of type $H\in M_N(A)$, having unitary entries, $H_{ij}\in U(A)$, and whose rows and columns are subject to orthogonality type conditions. Here $A$ can be any $C^*$-algebra, for instance $A=\mathbb C$,…
A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced…
I present a derivation of form factors in the Algebraic Cluster Model for an arbitrary number of identical clusters. The form factors correspond to representation matrix elements which are derived in closed form for the harmonic oscillator…
This chapter combines an introduction and research survey about Schubert varieties. The theme is to combinatorially classify their singularities using a family of polynomial ideals generated by determinants.
We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of Jack polynomials.
Thin sums matroids were introduced to extend the notion of representability to non-finitary matroids. We give a new criterion for testing when the thin sums construction gives a matroid. We show that thin sums matroids over thin families…