Complex matrix decomposition If I have a block matrix of complex matrices 
$$
\begin{bmatrix}
P  &Q\\
Q^T & P
\end{bmatrix}
$$ 
while Q being skew symmetric, the decomposition is 
$$
\begin{bmatrix}
I  & -iI\\
. & I
\end{bmatrix}
\begin{bmatrix}
P-iQ  & .\\
-Q & I
\end{bmatrix}
\begin{bmatrix}
I  & iI\\
. & P+iQ
\end{bmatrix}
$$
These are results from (R.A Wooding 1956).  Can anyone please explain what kind of complex decomposition is this or please provide any reference explaing this above decomposition. I have looked into Block LU decomposition but this does not explain how the above stated decomposition is working.
Appreciate your suggestions
!

Hint: the matrix valued function of a scalar $a$ : $$m(a) = \left[\begin{array}{cc}1&0\\a&1\end{array}\right]$$ has the property that $$m(a)\cdot m(b) = m(a+b)$$
and this property carries over to block form with $\bf I$ corresponding to $1$ and $\bf 0$ corresponding to $0$:
$$m({\bf A}) = \left[\begin{array}{cc}\bf I&\bf 0\\{\bf A}&{\bf I}\end{array}\right]$$
so that:
$$m({\bf A})m({\bf B}) = m({\bf A+B})$$
Hopefully this can help you gain some understanding.
