Is it possible to have the following sample correlation matrix for $x$, $y$, $z$?
$\begin{pmatrix} 1 & 0.8 & 0.2 \\ 0.8 & 1 & 0.7\\ 0.2 & 0.7 & 1\end{pmatrix}$
Where a 3 by 3 correlation matrix is $\begin{pmatrix} 1 & p_{xy} & p_{xz} \\ p_{yx} & 1 & p_{yz}\\ p_{zx} & p_{zy} & 1\end{pmatrix}$, and the $p$'s (partial correlations) are unequal, making this different more general than a similar question with equal partial correlations posed elsewhere.
My answer is yes, and my reasoning is: all the diagonal entries have value $1$, the matrix is symmetric and all entries are between $-1$ and $1$
Is my reasoning good enough? Are there other points that I'm missing?
