Show that 2 13 = 0 if and only if every linear combination aiX i is

Show that ρ

2 13 = 0 if and only if every linear combination aiX i

is uncorrelated with the quadratic form κi,jX iX j

. (Take κ

i = 0.) Show also that ρ

2 23 = 0 if and only if every linear combination aiX i

is uncorrelated with every quadratic form αijΧ

iΧ

j

.