Why isn't the set [MATH]F = \left \{ \begin{bmatrix}a & b\\ -\bar{b} & \bar{a}\end{bmatrix}: \space a,b \in \mathbb{C} \right \}[/MATH] a subspace of [MATH]M_{2\times 2}(\mathbb{C})[/MATH], if [MATH]M_{2\times 2}(\mathbb{C})[/MATH] is a vector space over [MATH]\mathbb{C}[/MATH]?
The matrix has weird formatting. The element with index 2,1 is [MATH]- \bar{b}.[/MATH]
The matrix has weird formatting. The element with index 2,1 is [MATH]- \bar{b}.[/MATH]