研究正定矩阵幂函数单调性的分析方法

Analytical Method to Study Monotonicity of Power Functions of Positive-definite Matrix

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1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.

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.