一类上三角分块矩阵的亚正定性

Metapositive Definiteness of a Class of the Upper Block Matrices

利用平方幂零矩阵的性质及矩阵的支撑理论,给出了3×3严格上三角分块矩阵A与半正定矩阵之和是亚半正定矩阵的充分条件。以及μI+A是亚正定矩阵的充分条件。并作了一些推广。

Let A be a 3×3 strict upper triangular block matrix and B be a symmetric semidefinite matrix. Base on the properties of square nilpontent matrices, the sufficient condition for A ＋ B to be metapositive emidefinite matrix and forμI ＋ B to be metapositive definte matrix is presented.