Abstract:  This paper has made the result of generalization and the answer according to the result of question raised in [1].
Especially we cancel the strong factors(A·B=B·A)in Theorerm 4 in [2]. We get the result to the same as the result of the inequality of Cauchy-Schwarz and Holder in the matrix. Finally,the paper also is a refinement of these two inequalities.It inserts the continuous integral value into the inequalities of matrix mean,and it becomes the inequality of integral form of continuous measure.

Key words: inequality, matrix trace, positive definite