I was wondering what is a standard textbook/source that I can reference this fact:
$\min_y \frac{1}{2} y^T C^{-1} y - b^T y$
such that $A^T y = f,$
where $C^{-1}$ is am $m \times m$ symmetric positive definite matrix, and $A$ is $m \times n$ matrix of rank $n \le m$. This quadratic constrained minimization problem has a unique solution given by the system
$$\begin{bmatrix} C^{-1} & A \\ A^T & 0 \end{bmatrix} \begin{bmatrix} y \\ \lambda \end{bmatrix} = \begin{bmatrix} b \\ f\end{bmatrix}.$$
I'm currently looking at these course notes Proposition 14.3 but would like a more established reference: https://www.cis.upenn.edu/~cis5150/cis515-12-sl14.pdf
Found in Section 10.1.1 of "Convex Optimization" by Boyd and Vandenberghe