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On eigenvectors of mixed graphs with exactly one nonsingular cycle

Yi-Zheng Fan (2007)

Czechoslovak Mathematical Journal

Let G be a mixed graph. The eigenvalues and eigenvectors of G are respectively defined to be those of its Laplacian matrix. If G is a simple graph, [M. Fiedler: A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory, Czechoslovak Math. J. 25 (1975), 619–633] gave a remarkable result on the structure of the eigenvectors of G corresponding to its second smallest eigenvalue (also called the algebraic connectivity of G ). For G being a general mixed graph with...

On eliminating transformations for nuisance parameters in multivariate linear model

Pavla Kunderová (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The multivariate linear model, in which the matrix of the first order parameters is divided into two matrices: to the matrix of the useful parameters and to the matrix of the nuisance parameters, is considered. We examine eliminating transformations which eliminate the nuisance parameters without loss of information on the useful parameters and on the variance components.

On elliptic curves and random matrix theory

Mark Watkins (2008)

Journal de Théorie des Nombres de Bordeaux

Rubinstein has produced a substantial amount of data about the even parity quadratic twists of various elliptic curves, and compared the results to predictions from random matrix theory. We use the method of Heegner points to obtain a comparable (yet smaller) amount of data for the case of odd parity. We again see that at least one of the principal predictions of random matrix theory is well-evidenced by the data.

On extremal positive maps acting between type I factors

Marcin Marciniak (2010)

Banach Center Publications

The paper is devoted to the problem of classification of extremal positive linear maps acting between 𝔅(𝒦) and 𝔅(ℋ) where 𝒦 and ℋ are Hilbert spaces. It is shown that every positive map with the property that rank ϕ(P) ≤ 1 for any one-dimensional projection P is a rank 1 preserver. This allows us to characterize all decomposable extremal maps as those which satisfy the above condition. Further, we prove that every extremal positive map which is 2-positive turns out to be automatically completely...

On feebly nil-clean rings

Marjan Sheibani Abdolyousefi, Neda Pouyan (2024)

Czechoslovak Mathematical Journal

A ring R is feebly nil-clean if for any a ∈ R there exist two orthogonal idempotents e , f ∈ R and a nilpotent w ∈ R such that a = e - f + w . Let R be a 2-primal feebly nil-clean ring. We prove that every matrix ring over R is feebly nil-clean. The result for rings of bounded index is also obtained. These provide many classes of rings over which every matrix is the sum of orthogonal idempotent and nilpotent matrices.

On Gaussian conditional independence structures

Radim Lněnička, František Matúš (2007)

Kybernetika

The simultaneous occurrence of conditional independences among subvectors of a regular Gaussian vector is examined. All configurations of the conditional independences within four jointly regular Gaussian variables are found and completely characterized in terms of implications involving conditional independence statements. The statements induced by the separation in any simple graph are shown to correspond to such a configuration within a regular Gaussian vector.

On generalized inverses of singular matrix pencils

Klaus Röbenack, Kurt Reinschke (2011)

International Journal of Applied Mathematics and Computer Science

Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate singular matrix pencils. The relations between the Kronecker structure of a singular matrix pencil and the...

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