For $n \in \mathbb{N}^*$, $A \in \mathcal{S}_n(\mathbb{R})$ and $i \in \llbracket 1; n \rrbracket$, we denote by $A^{(i)}$ the square matrix of order $i$ extracted from $A$, consisting of the first $i$ rows and the first $i$ columns of $A$.
Let $A$ be a matrix of $\mathcal{S}_n(\mathbb{R})$. Do we have the following equivalence:
$$A \text{ is positive} \quad \Longleftrightarrow \quad \forall i \in \llbracket 1; n \rrbracket, \operatorname{det}\left(A^{(i)}\right) \geqslant 0 ?$$