Mathematics for Economists

Constrained positive deÖnite matrixes

One can use the JacobiñSylvester criteria onC. To solve the su¢ ciency

problem one should check the determinants of thenpleading principal

minors ofC.

But to do this one should solve the equationBx= 0 and construct matrix

C.We want to avoid this and we will calculate the LASTnpleading

principal determinant of the bordered matrix

H$



0 B

BT A



.

The size ofHis(n+p)(n+p).(It is not obvious why does it work.

The proof is in the reader.)