论文标题
$ n $ am-matrices和几乎$ p $ - matrices的间隔船体
Interval hulls of $N$-matrices and almost $P$-matrices
论文作者
论文摘要
我们通过符号非反转属性建立了几乎$ p $ amatrices的表征。在这方面，我们的灵感来自$ n $ amatrices的类似结果。接下来，由$ \ mathbb {i}（a，a，b）$表示的两个$ m \ times n $矩阵$ a =（a_ {ij}）$和$ b =（b_ {ij}）$的$ a =（a_ {ij}）$是所有矩阵$ c \ in \ mathbb in \ mathbb in \ mathbb in \ mathbbbb {a，b）$是$ a_ {ij} $和$ b_ {ij} $的凸组合。使用符号非逆转属性，我们确定$ \ mathbb {i}（a，b）$的有限子集，该子集确定$ \ mathbb {i}（a，b）$中的所有矩阵是否是$ n $ - matrices/几乎$ p $ - matrices。这为整个类别的矩阵提供了测试，同时为$ n $ - matrices/近$ p $ - matrices。我们还为半阳性和最小半阳性矩阵建立了类似的结果。这些特征在精神上可能与Bialas-Garloff的$ P $ MATRICES相似[线性代数Appl。 1984]和Rohn-Rex [Simax 1996]，以及Rohn的正定矩阵[Simax 1994]。
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].
