Wavelet and Linear Algebra

Abstract A toeplitz matrix or diagonal-constant matrix is a matrix in which each descending diagonal from left to right is constant. A matrix $R$ is called integral row stochastic, if each row has exactly a nonzero entry, $+1$, and other entries are zero. In this  paper, we present $L$-rays of integral row stochastic toeplitz matrices, and  we provide an algorithm for constructing these matrices.

Abstract Let $x, y\in \mathbb{R}^n.$ We use the notation $x\prec_w y$ when $x$ is weakly majorized by $y$. We say that $x\prec_w y$ is decomposable at $k$ $(1\leq k < n)$ if $x\prec_w y$ has a coincidence at $k$ and $y_{k}\neq y_{k+1}$. Corresponding to this majorization we have a doubly substochastic matrix $P$. The paper presents $x\prec_w y$ is decomposable at some $k$ $(1\leq k<n)$ if and only if $P$ is of the form $D\oplus Q$ where $D$ and $Q$ are doubly stochastic and doubly substochastic matrices, respectively. Also, we write some algorithms to obtain $x$ from $y$ when $x\prec_w y$.

Abstract Miranda-Thompson majorization is a group-induced cone ordering on $\mathbb{R}^{n}$ induced by the group of generalized permutation with determinants equal to 1. In this paper, we generalize Miranda-Thompson majorization on the matrices. For $X$, $Y\in M_{m,n}$, $X$ is said to be  Miranda-Thompson majorized by $Y$ (denoted by $X\prec_{mt}Y$) if there exists some $D\in \rm{Conv(G)}$ such that $X=DY$.  Also, we characterize linear preservers of this concept on $M_{m,n}$.