نوع مقاله : مقاله پژوهشی
عنوان مقاله English
نویسندگان English
The square and real matricx $A$ is called a generalized row substochastic matrix, if the sum of the absolute values of the entries in each row is less than or equal to one.
Let $x,y\in \mathbb{R}^n$. We say that $x$ is right $B$-majorized (resp. left $B$-majorized) by $y$, denoted by $x \prec _{rB} y$ ($x \prec _{lB} y$), if there exists a substochastic matrix $D$, such that $x=yD$ (resp. $x=Dy$). In this article, we have found all the vectors such as $x$ that $x$ is right $B$-majorized (resp. left $B$-majorized) by $y$, for all row vector $y$ (resp. column vector). Also, we show $x \sim _{lB} y$ if and only if $\Vert x\Vert_\infty =\Vert y\Vert_\infty$ and prove $x \sim _{rB} y$ if and only if $\Vert x\Vert_1 =\Vert y\Vert_1$.
We have also created conditions in which the left $B$-majorization is equivalent to the left majorization, and created conditions in which the right $B$-majorization is equivalent to the right majorization.
کلیدواژهها English
