Re: definiteness of a quadratic form

In article <1162858558.676986.252450@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<analyst41@xxxxxxxxxxx> wrote:
Suppose we have a quadratic form x'Qx where

Q(i,j) = 0 if i = j

and

Case (1) Q(i,j) = 1 if i<>j

Case (2) Q(i,j) >=0 for i<> j.

Would appreciate any help to determine if the form is positive or
negative (semi) definite.

Thanks.


These are both indefinite forms. If X = (x y), then in case 1 the
form is 2xy, which can be positive or negative. In case 2 the form
is (a+b)xy, where a and b are positive, but which again can be either
positive or negative. It can't be definite in any higher dimension
because if you plug in the vectors (1 1 0 0 0 ...) and (1 -1 0 0 0 ...)
for X then it reduces to the 2-D case.

Of course the form is zero in one dimension...

--
Daniel Mayost

.

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