Related papers: The second production matrix of a Riordan array
If $A$ is an $n\times n$ matrix whose $n$ eigenvalues are ordered in terms of decreasing modules, $|\lambda_1 | \geq |\lambda_2| \geq ... |\lambda_n|$, it is often of interest to estimate $\frac{|\lambda_2|}{|\lambda_1|}$. If $A$ is a row…
N-matrices are real $n\times n$ matrices all of whose principal minors are negative. We provide (i) an $O(2^n)$ test to detect whether or not a given matrix is an N-matrix, and (ii) a characterization of N-matrices, leading to the recursive…
In this paper, we explore the concept of the ``matrix product of graphs," initially introduced by Prasad, Sudhakara, Sujatha, and M. Vinay. This operation involves the multiplication of adjacency matrices of two graphs with assigned labels,…
A formula for the number of toroidal m x n binary arrays, allowing rotation of the rows and/or the columns but not reflection, is known. Here we find a formula for the number of toroidal m x n binary arrays, allowing rotation and/or…
A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the…
We characterize the generator matrix in standard form of generalized Gabidulin codes. The parametrization we get for the non-systematic part of this matrix coincides with the $q$-analogue of generalized Cauchy matrices, leading to the…
The authors of this paper have used the theory of Riordan matrices to introduce the notion of a Riordan graph in \cite{CJKM}. Riordan graphs are proved to have a number of interesting (fractal) properties, and they are a far-reaching…
Modern datasets are often in the form of matrices or arrays,potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as…
Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…
A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…
Riordan matrices are infinite lower triangular matrices corresponding to the certain operators in the space of formal power series. Generalized Euler polynomials ${{g}_{n}}\left( x \right)={{\left( 1-x…
A natural definition of the product of infinite matrices mimics the usual formulation of multiplication of finite matrices with the caveat (in the absence of any sense of convergence) that the intersection of the support of each row of the…
An example of two $\mathbb R$-factorizable groups whose product is not $\mathbb R$-factorizable is constructed. One of these groups is second-countable and the other Lindel\"of to any finite power.
Form an $n \times n$ matrix by drawing entries independently from $\{\pm1\}$ (or another fixed nontrivial finitely supported distribution in $\mathbf{Z}$) and let $\phi$ be the characteristic polynomial. Conditionally on the extended…
We explore a data structure that generalises rectangular multi-dimensional arrays. The shape of an n-dimensional array is typically given by a tuple of n natural numbers. Each element in that tuple defines the length of the corresponding…
A unified approach to parametrization of the mixing matrix for $N$ generations is developed. This approach not only has a clear geometrical underpinning but also has the advantage of being economical and recursive and leads in a natural way…
Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. Associative arrays unify and simplify these different approaches into a common…
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends…
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…