Cones of diagonally dominant matrices
Cones of diagonally dominant matrices
复制标题
对角占优矩阵的锥体
DOI：
10.2140/pjm.1975.57.15
复制
发表时间：
1975
影响因子：
0.6
通讯作者：
D. Carlson
中科院分区：
文献类型：
--
作者：
G. P. Barker;D. Carlson
证明了复对角占优矩阵和真实的对角占优矩阵的几个锥的极值射线及其性质。给出了锥面格的几个结果。证明了Hermitian对角占优矩阵锥的对偶（在Hermitian矩阵的真实的空间中）不可能是半正定矩阵锥在任何非奇异线性变换下的像，特别是不可能是半正定矩阵锥在Ljaponian变换下的像，它由正稳定矩阵A确定.
The extreme rays of several cones of complex and real diagonally dominant matrices, and their duals, are identified. Several results on lattices of faces of cones are given. It is then shown that the dual (in the real space of hermitian matrices) of the cone of hermitian diagonally dominant matrices cannot be the image of the cone of positive semidefinite matrices under any nonsingular linear transformation; in particular, it cannot be the image of the cone of positive semidefinite matrices under the Ljapunov transformation ΈH AH+ HA* determined by a positive stable matrix A.