Mathematics for Economists

Constrained positive deÖnite matrixes

Observe thatx 2 =x 3 = 0 ,x 1 = 1 ,λ=0 is also a solution of the equations

x 2 x 3 + 2 λx 1 = 0

x 1 x 3 + 2 λx 2 = 0

x 1 x 2 + 2 λx 3 = 0

H=

0

BB

@

0 2 0 0

2 0 0 0

0 0 0 1

0 0 1 0

1

CC

A

The determinant is 4 which is not compatible with the max or the min rule.