If  where P is hermitian and Q is skew hermitian matrix P and Q are ?

Concept:

Hermitian Matrix:

Any square matrix say A is said to be a hermitian matrix if A = Aθ where Aθ is the transpose of the conjugate matrix of A.

Note: All the diagonal elements of a hermitian matrix is purely real.

Skew hermitian Matrix:

Any square matrix say A is said to be a skew hermitian matrix if A = - Aθ where Aθ is the transpose of the conjugate matrix of A.

Note: All the diagonal elements of a skew hermitian matrix is purely imaginary or zero.

Every square matrix say A can be uniquely expressed as sum of hermitian and skew hermitian matrix as shown below:

 where (A + Aθ) and (A - Aθ) are hermitian and skew hermitian matrices respectively. 

Calculation: 

Given:  where P is hermitian and Q is skew hermitian matrix

Here we have to find the matrix P and Q

As we know that, any square matrix can be be expressed as sum of hermitian and skew hermitian matrix.

i.e If A is a square matrix then A can be expressed as:  where (A + Aθ) and (A - Aθ) are hermitian and skew hermitian matrices respectively.