# Tagged: complex matrix

## 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.

## Problem 405

Recall that a complex matrix is called Hermitian if $A^*=A$, where $A^*=\bar{A}^{\trans}$.
Prove that every Hermitian matrix $A$ can be written as the sum
$A=B+iC,$ where $B$ is a real symmetric matrix and $C$ is a real skew-symmetric matrix.