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