Related papers: Pascal like matrices - an accessible factory of on…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…
In factoring matrices into the product of two matrices operations are typically performed with elements restricted to matrix subspaces. Such modest structural assumptions are realistic, for example, in large scale computations. This paper…
Matrices are built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums or multiplication of matrices are such procedures and a matrix built from these is said to be a {\em separable} matrix. A…
We consider a family of nonlinear recurrences with the Laurent property. Although these recurrences are not generated by mutations in a cluster algebra, they fit within the broader framework of Laurent phenomenon algebras, as introduced…
The study of the singularities and zeros of the generating functions of multiplicity distributions is advocated. Some hints from well known probability distributions and experimental data are given. The statistical mechanics analogies…
Given labeled data represented by a binary matrix, we consider the task to derive a Boolean matrix factorization which identifies commonalities and specifications among the classes. While existing works focus on rank-one factorizations…
We prove a family of identities, expressing generating functions of powers of characteristic polynomials of permutations, as finite or infinite products. These generalize formulae first obtained in a study of the geometry/topology of…
We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinatorial significance. For a specific subfamily, these…
In this paper, we will extend the falling and rising factorial transforms \cite{ref. 1} which in this case every arbitrary function can be applied. Then, the properties of these transforms will be investigated and some corollaries will be…
Consider $k\ge 2$ distinct, linearly independent, homogeneous linear recurrences of order $k$ satisfying the same recurrence relation. We prove that the recurrences are related to a decomposable form of degree $k$, and there is a very broad…
Bidiagonal matrices are widespread in numerical linear algebra, not least because of their use in the standard algorithm for computing the singular value decomposition and their appearance as LU factors of tridiagonal matrices. We show that…
Some identities that involve the elliptic version of the Cauchy matrices are presented and proved. They include the determinant formula, the formula for the inverse matrix, the matrix product identity and the factorization formula.
Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected…
Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$…
We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents…
It is known that a category of many-sorted algebras on pure sets of similarity type is "concretely equivalent" to a category of single-sorted algebras. In this paper, we characterize a single-sorted variety that corresponds to a many-sorted…
We give an overview about some elementary properties of Hoggatt matrices, which are generalizations of Pascal triangle, and study q-analogs and Fibonacci analogs and derive a common generalization.