A counting theorem in the semigroup of circulant Boolean matrices
A deflation formula for tridiagonal matrices
An explicit formula for the deflation of a tridiagonal matrix is presented. The resulting matrix is again tridiagonal.
A Deformed Quon Algebra
The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators , , on an infinite dimensional vector space satisfying the...
A determinant formula from random walks
One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute...
A determinant of Ostrowski.
A direct transformation between two fundamental matrix canonical forms
A duality based proof of the combinatorial nullstellensatz.
A Factorization of an Integral 2 x 2 Matrix Via a Rational Method.
A family of symmetric biadditive nonbilinear functions.
A family of tridiagonal pairs related to the quantum affine algebra .
A fast algorithm for solving regularized total least squares problems.
A Fiedler-like theory for the perturbed Laplacian
The perturbed Laplacian matrix of a graph is defined as , where is any diagonal matrix and is a weighted adjacency matrix of . We develop a Fiedler-like theory for this matrix, leading to results that are of the same type as those obtained with the algebraic connectivity of a graph. We show a monotonicity theorem for the harmonic eigenfunction corresponding to the second smallest eigenvalue of the perturbed Laplacian matrix over the points of articulation of a graph. Furthermore, we use...
A footnote on quaternion block-tridiagonal systems.
A formula for all minors of the adjacency matrix and an application
We supply a combinatorial description of any minor of the adjacency matrix of a graph. This description is then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of a graph G, whenever A(G) is invertible, where G is formed by replacing the edges of a tree by path bundles.
A formula for angles between subspaces of inner product spaces.
A formula for the eigenvalues of a compact operator
A free analogue of the transportation cost inequality on the circle
A functional equation for quadratic forms.
A further application of matrix analysis to communication structure in oceanic anthropology
A further investigation for Egoroff's theorem with respect to monotone set functions
In this paper, we investigate Egoroff’s theorem with respect to monotone set function, and show that a necessary and sufficient condition that Egoroff’s theorem remain valid for monotone set function is that the monotone set function fulfill condition (E). Therefore Egoroff’s theorem for non-additive measure is formulated in full generality.