实半正定方阵的性质(英文)

Properties of Real Positive Semidefinite Square Matrix

首先给出了有关实半正定方阵的若干性质,然后利用实半正定方阵的合同标准形,定义了合同根、第一对称数、第二对称数和第三对称数,并用它们刻画了实半正定方阵的张量积仍为半正定方阵的充分必要条件。

This paper is about to the positive semidefinite matrices.We first give some properties for these matrices.By applying the canonical form,we defined some concepts,they are the equivalent roots,the first symmetric number,the second symmetric number and the third symmetric number.Using these concept,we describe the necessary and sufficient conditions for the tensor product of positive semidefinite matrices to be positive semidefinite.