I've got the following system: $$ Q \left( \matrix{y\\x} \right) = \left( \matrix{b\\f} \right)$$
where $$Q = \left( \matrix{A \ B\\B^T \ C} \right) \in \mathbb R^{(n+m) \times (n+m)}$$ and $$ A \in \mathbb R^{n \times n}$$ regular, $$ B\in \mathbb R^{n \times m}, C \in \mathbb R^{m \times m}, b \in \mathbb R^{n}, f \in \mathbb R^{m}, x \in \mathbb R^{m}, y\in \mathbb R^{n}$$
What's a correct formula for the solution for y in dependance of $$ A^{-1}, B, b, x$$?
Thanks a lot for any help!
$Q(\matrix{y\\x}) = (\matrix{b\\f}) \iff b=Ay+Bx$ and $f=B^Ty+Cx$.
From $ b=Ay+Bx $ we get $y=A^{-1}(b-Bx)$.