关于准次正定矩阵

On the Almost Positive Subdefinite Matrices

研究准次正定矩阵的性质及行列式理论.得到了判定准次正定矩阵的几个充要条件,以及准次正定矩阵的几个行列式不等式.并将著名的Fejer定理、Minkowski不等式及Hadamard不等式拓广到了准次正定阵上,扩大了Minkowski不等式的指数范围.

The properties and determinant theories of the almost positive subdefinite matrix and determinant are discussed. The judging by seven necessary and sufficient conditions and five determinant inequalities of almost positive subdefinite matrix is established. As applications, some famous theorems and inequalities named after Fejer, Minkowski and Hadamard are generalized, and the index scope of Minkowski inequality is enlarged.