On convexity of polynomial paths and generalized majorizations.
On convexity, the Weyl group and the Iwasawa decomposition
On corepresentations of equipped posets and their differentiation.
On Davis-Kahan-weinberger Extension Theorem
On decomposition of k-tridiagonal ℓ-Toeplitz matrices and its applications
We consider a k-tridiagonal ℓ-Toeplitz matrix as one of generalizations of a tridiagonal Toeplitz matrix. In the present paper, we provide a decomposition of the matrix under a certain condition. By the decomposition, the matrix is easily analyzed since one only needs to analyze the small matrix obtained from the decomposition. Using the decomposition, eigenpairs and arbitrary integer powers of the matrix are easily shown as applications.
On Definiteness Of Certain Matrix Functions Of A Matrix
On determinant preservers over skew fields.
On determining minimal spectrally arbitrary patterns.
On diagonalization by dynamic output feedback
On dimension formulas for representations.
On distance Laplacian energy in terms of graph invariants
For a simple connected graph of order having distance Laplacian eigenvalues , the distance Laplacian energy is defined as , where is the Wiener index of . We obtain a relationship between the Laplacian energy and the distance Laplacian energy for graphs with diameter 2. We obtain lower bounds for the distance Laplacian energy in terms of the order , the Wiener index , the independence number, the vertex connectivity number and other given parameters. We characterize the extremal graphs...
On eigenvectors of mixed graphs with exactly one nonsingular cycle
Let be a mixed graph. The eigenvalues and eigenvectors of are respectively defined to be those of its Laplacian matrix. If 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 corresponding to its second smallest eigenvalue (also called the algebraic connectivity of ). For being a general mixed graph with...
On elementary symmetric functions of the eigenvalues of the sum and product of normal matrices
On eliminating transformations for nuisance parameters in multivariate linear model
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 existence of hyperinvariant subspaces for linear maps.
On extremal positive maps acting between type I factors
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
A ring is feebly nil-clean if for any there exist two orthogonal idempotents and a nilpotent such that . Let be a 2-primal feebly nil-clean ring. We prove that every matrix ring over 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 Fixed Point Linear Equations.
On Fueter-Hurwitz regular mappings [Book]
On Gaps Between Bounded Operators