In: Advanced Math
lets a matrix A = 1 2 3
2 5 4
3 4 9
Here all diagonal entries are positive.
and let check positive definite or not.
Method :1
Check the determinants of all upper- left submatrices are positive or not.
Method :2.
If A matrix is positive definite if it's symmetric and all its eigenvalues are positive.
From both the method we get to know that That given A is not positive definite or negatively definite with non-negative diagonal elements of A.
Thank you.