Prove that the magnitude of determinant of a unitary transform is unity. Also show that all the eigenvalues of a unitary matrix have unity magnitude
Show that the entropy of an N x 1 Gaussian random vector u with mean p. and covariance R. given by
![2386_371332f5-769e-4f6c-877c-c565d0b5279d.png](https://secure.tutorsglobe.com/CMSImages/2386_371332f5-769e-4f6c-877c-c565d0b5279d.png)
is invariant under any unitary transformation