```markdown
### Image Description

**Title:** Equality Constrained Quadratic Minimization

- **Objective:** Minimize the function \((1/2)x^T P x + q^T x + r\)
- **Constraint:** Subject to \(Ax = b\)

**Optimality Condition:**

\[
\begin{bmatrix}
P & A^T \\
A & 0
\end{bmatrix}
\begin{bmatrix}
x^* \\
\nu^*
\end{bmatrix}
=
\begin{bmatrix}
-q \\
b
\end{bmatrix}
\]

- **Notes:**
  - The coefficient matrix is called the KKT matrix.
  - The KKT matrix is nonsingular if and only if:
    \[
    Ax = 0, \, x \neq 0 \implies x^T P x > 0
    \]
  - Equivalent condition for nonsingularity: \(P + A^T A \succ 0\)

**Source:** A. d'Aspremont, Convex Optimization M2. (Slide 36/53)
```
