Related papers: Double Circulant Matrices
We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a…
The higher rank numerical ranges of generic matrices are described in terms of the components of their Kippenhahn curves. Cases of tridiagonal (in particular, reciprocal) 2-periodic matrices are treated in more detail.
In this paper, we introduce the dual $r$-rank decomposition of dual matrix, get its existence condition and equivalent form of the decomposition, as well as derive some characterizations of dual Moore-Penrose generalized inverse(DMPGI).…
In this paper, we give upper and lower bounds for the spectral norms of r-circulant matrices with the generalized bi-periodic Fibonacci numbers. Moreover, we investigate the eigenvalues and determinants of these matrices.
An integrable deformation of the known integrable model of two interacting p-dimensional and q-dimensional spherical tops is considered. After reduction this system gives rise to the generalized Lagrange and the Kowalevski tops. The…
When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…
A binary matrix can be scanned by moving a fixed rectangular window (submatrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
We consider Riordan arrays $\bigl(1/(1-t^{d+1}), ~ tp(t)\bigr)$. These are infinite lower triangular matrices determined by the formal power series $1/(1-t^{d+1})$ and a polynomial $p(t)$ of degree $d$. Columns of such matrix are eventually…
In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…
In this paper, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear combinations of the entries in the first row with integer…
The notion of disjoint weighing matrices is introduced as a generalization of orthogonal designs. A recursive construction along with a computer search lead to some infinite classes of disjoint weighing matrices, which in turn are shown to…
We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.
We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…
We obtain, using exponential quadratic sums, explicit expressions for the number of double persymmetric matrices with entries in F_2 of given rank. (A matix [a(i,j)) is persymmetric if a(i,j) = a(r,s) for i+j = r+s)
We classify all cyclotomic matrices over real quadratic integer rings and we show that this classification is the same as classifying cyclotomic matrices over the compositum all real quadratic integer rings. Moreover, we enumerate a related…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…
Circulant matrices over finite fields and over commutative finite chain rings have been of interest due to their nice algebraic structures and wide applications. In many cases, such matrices over rings have a closed connection with diagonal…