Eigenvalue Interlacing for Certain Classes of Matrices with Real Principal Minors
Eigenvalue Interlacing for Certain Classes of Matrices with Real Principal Minors
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DOI：
10.1016/0024-3795(87)90117-0
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发表时间：
1987-04
影响因子：
1.1
通讯作者：
D. Hershkowitz;V. Mehrmann;H. Schneider
中科院分区：
文献类型：
--
作者：
D. Hershkowitz;V. Mehrmann;H. Schneider
考虑了z矩阵和厄米矩阵的两个共同性质：(1)特征值的交错性，即矩阵的两个最小实特征值被任何小于一阶的主子矩阵的最小实特征值所交错。(2)正的GLP性质，即如果一个矩阵有一个正的广义主次阵序列，则该矩阵的所有主次阵都是正的。这些属性之间的关系以及相关的属性一般检查。
Two common properties of Z-matrices and Hermitian matrices are considered: (1) The eigenvalue interlacing property, i.e., the two smallest real eigenvalues of a matrix are interlaced by the smallest real eigenvalue of any principal submatrix of order one less. (2) The positive GLP property, i.e., if a matrix has a positive sequence of generalized leading principal minors, then all the principal minors of the matrix are positive. The relationship between these properties as well as related properties is examined in general.