Constrained positive deÖnite matrixes
A maximal solution is whenx 1 =x 2 =x 3 = 1 /p
3 in this caseλ= x 21 xx^2
3= ^1
2
p
3H=
0
BB
@
0 2 /
p
3 2/p
3 2/p
3
2 /p
3 1 /p
3 1/p
3 1/p
3
2 /p
3 1/p
3 1 /p
3 1/p
3
2 /p
3 1/p
3 1/p
3 1 /p
31
CC
A
The determinant is ^163 .As there are three variables this is the right sign
condition for the maximum as 1 =( 1 )^3