1. The problem statement, all variables and given/known data I have the matrix A = [-10 3.5 3; 3.5 -4 0.75; 3 0.75 -0.75] I need to determine whether this is negative semidefinite. 2. Relevant equations 3. The attempt at a solution 1st order principal minors: -10 -4 -0.75 2nd order principal minors: 2.75 -1.5 2.4375 3rd order principal minor: =det(A) = 36.5625 To be negative semidefinite principal minors of an odd order need to be ≤ 0, and ≥0 fir even orders. This suggests that the matrix is not negative semidefinite. I don't believe my answer though for two reasons: - I thought that if the diagonal entries were all negative that meant it was negative semidefinite? - I am looking at the Hessian of an expenditure function and the expenditure function satisfies all the other conditions of being an expenditure function, so I think it should be negative semi definite. Where have I gone wrong?