Every Complex Matrix Can Be Written as $A=B+iC$, where $B, C$ are Hermitian Matrices
Problem 425
(a) Prove that each complex $n\times n$ matrix $A$ can be written as
\[A=B+iC,\]
where $B$ and $C$ are Hermitian matrices.
(b) Write the complex matrix
\[A=\begin{bmatrix}
i & 6\\
2-i& 1+i
\end{bmatrix}\]
as a sum $A=B+iC$, where $B$ and $C$ are Hermitian matrices.
