Thursday, 10 May 2012

Unitary and Orthonormal Matrix

Let the Matrix $U \in \mathbb{C}^{N \times N}$ is Unitary. Define $\widetilde{U} \in \mathbb{R}^{2N \times 2N}$ as:

$$\widetilde{U}=\begin{bmatrix} Re(U) & -Im(U)\\ \\ Im(U)& Re(U) \end{bmatrix}$$

Prove that $\widetilde{U}$ is Orthonormal