几类矩阵的亚正定性判定

THE DECISION ON SOME CLASSES OF POSITIVE METADEFINITE MATRIX

引入完全严格对角占优矩阵的概念，证明了具有正对角元的，完全严格对称角占优矩阵，迹占优矩阵及广义反对称矩阵都是亚正定的；并利用Ｒａｙｌｅｉｇｈ商与特征值的关系，获得亚正定矩的特征值实部的范围．

The concept of totally strict diagonal do minant matrix was introduced. Totally strict diagonal dominant,trace dominant and generalized antisymmetric matrices with positive diagona elements were proofed to be positive metadefinitive. The range of the real part of eigenvalue for sum of positive metadefinite matrices was estimated from the relationship of Rayleigh quotient with eigenvalue.