positive definite matrix interval Hi could you help me with following
$$
\begin{pmatrix}
1 & a & a \\
a & 1 & a \\
a & a & 1
\end{pmatrix}
$$
is a $3 \times 3$ matrix.
Find the largest interval for a such that this matrix is positive definite.
How to do this??
Thanks a lot!

Hint: a matrix is positive definite if and only if its leading principal minors are all positive. In your case, this means your matrix is positive definite iff the three quantities
$$
1,\ \det\begin{pmatrix}1&a\\a&1\end{pmatrix},\ \det\begin{pmatrix}1&a&a\\a&1&a\\a&a&1\end{pmatrix}
$$
are all positive.
