Related papers: Elementary triangular matrices and inverses of $k$…
Given complex parameters $x$, $\nu$, $\alpha$, $\beta$ and $\gamma \notin -\mathbb{N}$, consider the infinite lower triangular matrix $\mathbf{A}(x,\nu;\alpha, \beta,\gamma)$ with elements $$ A_{n,k}(x,\nu;\alpha,\beta,\gamma) =…
If $A$ is a tridiagonal matrix, then the equations $AX=I$ and $XA=I$ defining the inverse $X$ of $A$ are in fact the second order recurrence relations for the elements in each row and column of $X$. Thus, the recursive algorithms should be…
We consider discretizations of the hyper-singular integral operator on closed surfaces and show that the inverses of the corresponding system matrices can be approximated by blockwise low-rank matrices at an exponential rate in the block…
This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the…
EP Banach space operators and EP Banach algebra elements are characterized using different kinds of factorizations. The results obtained generalize well-known characterizations of EP matrices, EP Hilbert space operators and EP $C^*$-algebra…
Commutative hypercomplex algebras offer significant advantages over traditional quaternions due to their compatibility with linear algebra techniques and efficient computational implementation, which is crucial for broad applicability. This…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
This paper investigates prime and co-prime integer matrices and their properties. It characterizes all pairwise co-prime integer matrices that are also prime integer matrices. This provides a simple way to construct families of pairwise…
This paper shows how to obtain a simple closed form for the elements of a triangular matrix raised to the nth power.
In this work we deduce explicit formulae for the elements of the matrices that represent the action of integro-differential operators over the coefficients of generalized Fourier series. Our formulae are obtained by performing operations on…
We present explicit formulas for Moore-Penrose inverses of some families of set inclusion matrices arising from sets, vector spaces, and designs.
A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…
Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not been…
In this paper, various properties of core-EP matrices are investigated. We introduce the MPDMP matrix associated with $A$ and by means of it, some properties and equivalent conditions of core-EP matrices can be obtained. Also, properties of…
We present new properties of generalized core-EP inverse in a Banach *-algebra. We characterize this new generalized inverse by using involved annihilators. The generalized core-EP inverse for products is obtained. The core-EP orders for…
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
In this paper we express the eigenvalues of real anti-tridiagonal Hankel matrices as the zeros of given rational functions. We still derive eigenvectors for these structured matrices at the expense of prescribed eigenvalues.
In this paper, we introduce the notation of $E$-weighted core-EP and $F$-weighted dual core-EP inverse of matrices. We then obtain a few explicit expressions for the weighted core-EP inverse of matrices through other generalized inverses.…