关于一道硕士研究生入学试题的推广

On Generalization of a Question of Entrance Test for MA Candidates

2004年漳州师范学院硕士研究生入学考试中有一道高等代数试题,是关于实对称阵的所有正特征根之和与其迹所确定的不等式。证明了这个不等式可推广到实矩阵上去,即实矩阵的所有实部为正的特征根之和与其迹也有类似不等式,同时给出了其等号成立的充要条件。

In Entrance Test of Higher Algebra of Zhangzhou Terachers Colleage for MA/MS Candidates in 2004, there is a question on inequality, which is determined by the summation of all positive eigenvalues of real symmetric matrix and its trace. This paper proves that this inequality can be generalized in real matrix, i.e. , there is a similar inequality for the summation of all positive real part of eigenvalues of real matrix and its trace, and we also give the necessary and sufficient conditions for the equality.