Finding infinum and supremum of over the quadratic q(x)

Let A denote the matrix

A=

1 1 -12

-1 1 0

0 0 2

and define the quadratic

q(x):= <x,Ax>

where<> defines the inner product

Determine the supremum and infimum of q(x) over all unitx vectors x

By definiton we know that the infinum and supremum are interrelated by being the smallest and largest numbers that are less than all elements or greater than all elements in a set t.

I am a bit confused since x is only unit so its range of values should not be infinite (so my logic tells me) and this is the time we use the infimum and supremum.

I am having trouble starting the problem.

Thank you very much for any help,

-Carlos

Re: Finding infinum and supremum of over the quadratic q(x)

If you multiply it out, you'll get that q(x,y,z) is a polynomial in the three variables. You want to find the extrema in 3-space subject to the constraint x^2+y^2+z^2=1. Check out "Lagrange multipliers" for a method.