Let A denote the matrix

A=

1 1 -12and define the quadratic

-1 1 0

0 0 2

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