## 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.