中文摘要：

偕正矩阵在矩阵论的理论和应用两方面都很重要，这种类型的矩阵常出现在最优化理论的研究与应用中．近年来，许多文章都在研究判定一个已知的（实）对称矩阵是或不是偕正矩阵、是或不是严格偕正矩阵的方法．本文侧重于研究判定对称矩阵是（严格）偕正矩阵的充分条件及对称矩阵不是偕正矩阵的充分条件，并得出几个肯定性结果．与文[7]的方法相比较，我们的判定已知对称矩阵偕正性的方法要简单易行得多．

英文摘要：

The copostive matrices are very important in both research and applications of matrix theory. This kind of matrices often occur in optimization theory. Recently many papers explored ways of determining whether a given symmetric matrix is copositive. This paper establishes some sufficient conditions for a given symmetric matrix to be a copositive matrix or a strictly copositive matrix. We also establish some sufficient conditions determining that a given symmetric matrix is not a copositive matrix. In comparison with the method of article[ 7 ] our method is much easier to use.