Sylvester's criterion states that a Hermitian matrix 
is positive
definite iff the determinants
of all upper-left square submatrices of 
are positive. In particular, it applies to a real symmetric
matrix.
Sylvester's Criterion
See also
Positive Definite MatrixExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Sylvester's Criterion." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SylvestersCriterion.html