**In minisymposium: Geometry and Order Structure in Matrices and Operators**

The matrix $M$= $\left[\begin{array}{cc} A & X \ X^\ast & B% \end{array}% \right]$ is called PPT matrix if the matrices $\left[\begin{array}{cc} A & X \ X^\ast & B% \end{array}% \right]$ and $\left[\begin{array}{cc} A & X^\ast \ X & B% \end{array}% \right]$ are both positive semi definite.

Let A,B be $n\times n$ positive definite matrices. Then arithmetic, geometric and harmonic means of these matrices are $\frac{1}{2}\left(A+B\right)$, $A^{1/2}\left(A^{-1/2}BA^{-1/2}\right)^{1/2}A^{1/2}$ and $2\left(A^{-1}+B^{-1}\right)^{-1}$ respectively.

In this talk we obtain some good results related to positive definite matrices by using properties of PPT matrix, Matrix means and majorization.