Constrained positive deÖnite matrixes
Ifx 1 =x 2 = 1 /p
2 thenλ= 1 /p
2A=
p
2 0
0 p
2,B=
2 /
p
2 , 2 /p
2,H=
0
@
0
p
2p
p^2
2 p
p 2 0
2 0 p
21
A
det(H)= 4p
2 .As there are two variables this is the condition for local
maximum, sop^1
2 ,
p^1
2is a local maximum.