$N$ -矩阵和几乎$P$ -矩阵的区间壳
Interval hulls of $N$-matrices and almost $P$-matrices
摘要：
我们通过一个符号不可逆性质建立了几乎$P$ -矩阵的一个特征。在这一点上，我们的灵感来自类似的结果$N$ -矩阵。接下来，由$\mathbb{I}(A,B)$表示的两个$m \times n$矩阵$A=(a_{ij})$和$B = (b_{ij})$的区间壳是所有矩阵$C \in \mathbb{R}^{m \times n}$的集合，使得每个$c_{ij}$是$a_{ij}$和$b_{ij}$的凸组合。利用符号不可逆性质，我们确定了$\mathbb{I}(A,B)$的一个有限子集，它决定了$\mathbb{I}(A,B)$中的所有矩阵是否都是$N$ -矩阵/几乎$P$ -矩阵.这提供了一个测试，为整个类的矩阵同时是$N$ -矩阵/几乎$P$ -矩阵。对于半正矩阵和极小半正矩阵，我们也建立了类似的结果。这些特征可以被认为在精神上类似于Bialas-Garloff [ Linear Algebra Appl.1984]和Rohn-Rex [SIMAX 1996]的PDMATHAMM-矩阵，以及Rohn [SIMAX 1994]的正定矩阵。
英文摘要：
We establish a characterization of almost $P$-matrices via a sign non-reversal property. In this we are inspired by the analogous results for $N$-matrices. Next, the interval hull of two $m \times n$ matrices $A=(a_{ij})$ and $B = (b_{ij})$, denoted by $\mathbb{I}(A,B)$, is the collection of all matrices $C \in \mathbb{R}^{m \times n}$ such that each $c_{ij}$ is a convex combination of $a_{ij}$ and $b_{ij}$. Using the sign non-reversal property, we identify a finite subset of $\mathbb{I}(A,B)$ that determines if all matrices in $\mathbb{I}(A,B)$ are $N$-matrices/almost $P$-matrices. This provides a test for an entire class of matrices simultaneously to be $N$-matrices/almost $P$-matrices. We also establish analogous results for semipositive and minimally semipositive matrices. These characterizations may be considered similar in spirit to that of $P$-matrices by Bialas-Garloff [Linear Algebra Appl. 1984] and Rohn-Rex [SIMAX 1996], and of positive definite matrices by Rohn [SIMAX 1994].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
