Since the numerical coefficient (in the definition of ) is clearly positive, you are trying to show that the matrix is positive for a certain value of , where
(Here, I have used in place of your , and I have used the fact that to rewrite the entries below the diagonal.)
In fact, the matrix is positive for all values of . The quickest way to see this is to use complex numbers and to write . Then the complex conjugate and the inverse of are equal: . Also, . Define a matrix by . Then is an matrix whose -element is (for and ). The matrix has -element which is equal to the -element of .
Therefore . But any matrix of the form is positive, so it follows that is positive.