for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

In this paper, some properties of $alpha$-skew Armendariz and central Armendariz rings have been studied by variety of others. We generalize the notions to central $alpha$-skew Armendariz rings and investigate their properties. Also, we show that if $alpha(e)=e$ for each idempotent $e^{2}=e in R$ and $R$ is $alpha$-skew Armendariz, then $R$ is abelian. Moreover, if $R$ is central $alpha$-skew A...

In this paper, skew ABC matrix and its energy are introduced for digraphs. Firstly, some fundamental spectral features of the digraphs established. Then upper lower bounds presented Further extremal determined attaining these bounds.

We say that a square complex matrix is condensable if it can be reduced to a bandform through a nite sequence of elementary uni-tary similarities. The two main results of this paper are the following assertions: (1) Any matrix with a low rank skew-Hermitian part is condens-able. (2) If A is a normal condensable matrix, then any rank one perturbation of A (generally nonnormal) is condensable as ...

The multivariate Student-t copula family is used in statistical finance and other areas when there is tail dependence in the data. It often is a good-fitting copula but can be improved on when there is tail asymmetry. Multivariate skew-t copula families can be considered when there is tail dependence and tail asymmetry, and we show how a fast numerical implementation for maximum likelihood esti...

Two matrix vector spaces V,W⊂Cn×n are said to be equivalent if SVR=W for some nonsingular S and R. These congruent R=ST. We prove that all matrices in V W symmetric, or skew-symmetric, then only they equivalent. Let F:U×…×U→V G:U′×…×U′→V′ symmetric skew-symmetric k-linear maps over C. If there exists a set of linear bijections φ1,…,φk:U→U′ ψ:V→V′ transforms F G, such with φ1=…=φk.

Two algorithmic techniques for specifying the existence of a k×k submatrix with elements 0,±1 in a skew and symmetric conference matrix of order n are described. This specification is achieved using an appropriate computer algebra system.

In this note, we consider the problem of computing the exponential of a real matrix. It is shown that if A is a real n × n matrix and A can be diagonalized over C, then there is a formula for computing e involving only real matrices. When A is a skew symmetric matrix, the formula reduces to the generalization of Rodrigues’s formula given in Gallier and Xu [1].