Hi,

I have a matrix of the form $A=VDV^H$, where $V$ is a $M \times 2M$ complex matrix, $D$ is a $2M \times 2M$ diagonal real matrix, thus the dimension of $A$ is $M \times M$.

My problem is how to maximize the determinant of $A$ by choosing the diagonal $D$ (suppose the sum of diagonals of $D$ equals to $1$)?

Since the dimension of $V$ is $M \times 2M$, I don't know how to solve this problem. Thanks.