Related papers: Closed forms for powers and inverses of special ma…
Permutations can be represented as linear combinations of natural numbers with different powers. In this paper, its coefficient matrix and inverse matrix is derived, and the results show the coefficient matrix is a lower triangular matrix…
Special matrix functions have recently been investigated for regions of convergence, integral representations and the systems of matrix differential equation that these functions satisfy. In this paper, we find the recursion formulas for…
In this paper, we obtain a general expression for the entries of the r. (r is integer) power of a certain n-square complex tridiagonal matrix. In addition, we get the complex factorizations of Fibonacci polynomials, Fibonacci and Pell…
Square matrices of the form $\widetilde{\mathbf{A}} =\mathbf{A} + \mathbf{e}D \mathbf{f}^*$ are considered. An explicit expression for the inverse is given, provided $\widetilde{\mathbf{A}}$ and $D$ are invertible with…
In this article one-sided (b, c)-inverses of arbitrary matrices as well as one-sided inverses along a (not necessarily square) matrix, will be studied. In adddition, the (b, c)-inverse and the inverse along an element will be also…
This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.
This paper gives new explicit formulas for sums of powers of integers and their reciprocals.
A concise analytical formula is developed for the inverse of an invertible 3 x 3 matrix using a telescoping method, and is generalized to larger square matrices. The formula is confirmed using randomly generated matrices in Matlab
In this paper, by means of the classical Lagrange inversion formula, we establish a general nonlinear inverse relations which is a partial solution to the problem proposed in the paper [J. Wang, Nonlinear inverse relations for the Bell…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
We give a systematic construction of inverse-closed (Banach) subalgebras in general higher-dimensional non-commutative tori
We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…
Triangular numbers that are multiple of other triangular numbers are investigated. It is known that for any positive non-square integer multiplier, there is an infinity of multiples of triangular numbers which are triangular numbers. If the…
New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences.…
We present the transformation of several sums of positive integer powers of the sine and cosine into non-trigonometric combinatorial forms. The results are applied to the derivation of generating functions and to the number of the closed…
By using the piecewise method, Lagrange interpolation formula and Lucas' theorem, we determine explicit expressions of the inverses of a class of reversed Dickson permutation polynomials and some classes of generalized cyclotomic mapping…
For any complex parameters $x$ and $\nu$, we provide a new class of linear inversion formulas $T = A(x,\nu) \cdot S \Leftrightarrow S = B(x,\nu) \cdot T$ between sequences $S = (S_n)_{n \in \mathbb{N}^*}$ and $T = (T_n)_{n \in…
A closed form expression for the three-electron Hylleraas integral involving the inverse quadratic power of one inter-particle coordinate is obtained, and recursion relations are derived for positive powers of other coordinates. This result…
In this paper, we derive the general expression of the r-th power for some n-square complex tridiagonal matrices. Additionally, we obtain the complex factorizations of Fibonacci polynomials.
We present here the necessary and sufficient conditions for the invertibility of tridiagonal matrices, commonly named Jacobi matrices, and explicitly compute their inverse. The techniques we use are related with the solution of…