This is what we are given in the assignment:
Recall a definition of scalar product on complex numbers. Let A = [[3,1],[1,2]]. Prove that the product as defined by:
* => dot product
u * v := uT * A * conjugate(v)
( = Sum from i,j=1 to 2; uiAijconjugate(vj) )
is a scalar product on C according to the definition.
We are give that the following equation will be useful:
2(ac) >= -a2 -c2 for all a,c as elements of R
The Attempt at a Solution
There are many of us working on this and we were not even sure exactly how to start this problem. It is trivial to prove the Sum given is equal to uT * A * conjugate(v). But from there we weren't sure exactly what else to prove.
Any help would be extremely appreciated