Positive Definite and Hermitian Matrices If we know that $C$ is positive definite and Hermitian, how can we prove that there exists a matrix $Q$ such that $Q^∗CQ=I$. Where, $Q^∗$ is complex conjugate.
The definition of positive definiteness for a Hermitian Matrix I am using is if all principal minors are positive.
I am also looking for a link between this definition and another equivalent definition i.e. $x^*Ax>0$ for all $x$.

Hint: if $C$ is positive definite, then there is a unitary matrix $U$ for which $C = UDU^*$ where
$$
D = \pmatrix{\lambda_1 &&\\&\ddots&\\ &&\lambda_n}
$$
is the diagonal matrix of eigenvalues (note that $\lambda_i > 0$).  Find a matrix $V$ for which 
$$
VDV^* = \pmatrix{1 &&\\&\ddots&\\ &&1}
$$
(hint: there is a diagonal $V$ that works here). Now we have $D = UCU^*$, and $I = V^*DV$.  It follows that $I = V^*UCU^*V = (U^*V)^*C(U^*V)$
