分块矩阵的2个新的特征值包含定理
Two new eigenvalue inclusion theorems for partitioned matrices
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摘要: 将双1-矩阵和双2-矩阵概念推广到分块矩阵，定义了块双1-矩阵和块双2-矩阵，给出了它们的充要条件，并由此获得2个新的矩阵特征值包含区域，证明了新的特征值包含区域含于经典的分块矩阵Gerschgorin特征值包含区域和分块矩阵Brauer特征值包含区域，因而能更精确地确定矩阵特征值的位置. Abstract: We extend the definitions of doubly 1-matrices and doubly 2-matrices to partitioned matrices respectively,and present block doubly 1-matrices and block doubly 2-matrices.By studying their sufficient and necessary conditions,two new eigenvalue inclusion regions are given,and proved to be tighter than the well known Gerschgorin eigenvalue inclusion region and Brauer eigenvalue inclusion region for partitioned matrices.
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