I've made a recent post where I tried to define any square matrix \(\displaystyle A_n \in \mathbb{C}\) as the sum of a symetric and a skew symetric matrix.
The same principle aplies to defining \(\displaystyle A \) as the sum of hermitian and skew hermitian matrices.
Now, when trying to define a square matrix \(\displaystyle A_n \in \mathbb{C}\) as \(\displaystyle A = B + iC\), with \(\displaystyle A, B\) being both hermitian matrices I'm completly stuck.
I tried re-applying the logic, but I can't find any matrix \(\displaystyle C\) that satisfies the requirements.
The same principle aplies to defining \(\displaystyle A \) as the sum of hermitian and skew hermitian matrices.
Now, when trying to define a square matrix \(\displaystyle A_n \in \mathbb{C}\) as \(\displaystyle A = B + iC\), with \(\displaystyle A, B\) being both hermitian matrices I'm completly stuck.
I tried re-applying the logic, but I can't find any matrix \(\displaystyle C\) that satisfies the requirements.