Sylvester's criterion

Sylvester's criterion is a mathematical principle used to determine whether a given real symmetric matrix is positive definite. According to Sylvester's criterion, a real symmetric matrix \( A \) is positive definite if and only if all of its leading principal minors (the determinants of the top-left \( k \times k \) submatrices for \( k = 1, 2, \ldots, n \), where \( n \) is the order of the matrix) are positive.