中文摘要：

文章用数学分析的方法研究了对于正定矩阵的幂次方的单调性．具体地，当指数为小于l的正数时，正定矩阵幂函数是严格单调增加的，而当指数大于1时，正定矩阵幂函数不具有单调性．

英文摘要：

We use mathematical analysis to study the proved that a power function of positive-definite matrix is while it is not monotonic if the power is bigger than 1. monotonicity of power functions of positive-definite matrix. It is increasing strictly if the power is a positive numbere less than 1.