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.
A generalization of a theorem of Boolean relation matrices
A Generalization of Cayley's Theorem.
A generalization of group difference sets and the matrix equation Am = dI + ...J.
A generalization of Moore-Penrose biorthogonal systems.
A generalization of rotations and hyperbolic matrices and its applications.
A generalization of the exterior product of differential forms combining Hom-valued forms
This article deals with vector valued differential forms on -manifolds. As a generalization of the exterior product, we introduce an operator that combines -valued forms with -valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.
A Generalization of the Matrix-Tree Theorem.
A geometric approach for testing regularity of multi-dimensional polynomial matrices and a pencil of -matrices
A geometric construction for spectrally arbitrary sign pattern matrices and the -conjecture
We develop a geometric method for studying the spectral arbitrariness of a given sign pattern matrix. The method also provides a computational way of computing matrix realizations for a given characteristic polynomial. We also provide a partial answer to -conjecture. We determine that the -conjecture holds for the class of spectrally arbitrary patterns that have a column or row with at least nonzero entries.
A geometric maximization problem