Mathematics for Economists

Constrained positive deÖnite matrixes

For the third root



p^12 ,p^12



,λ= 1 / 2

H=

0

@

0 2 /

p

2 2/

p

2

 2 /

p

2 1 1

2 /

p

2 1 1

1

A

det (H)= 8 .Asp=1 the sign for minimum must be 1 =( 1 )p,so

p^12 ,p^12



is a local minimum.