This might not be very difficult, but I think I may have gotten a little confused.

Suppose we are given a matrix A, and would like to find the vector x of modulus 1 which maximises the product xt A x (xtranspose times A times x) Consider the following iteration: We start with some vector y of modulus 1, find the vector z of modulus 1 which maximises zt A y, and then put y=z and continue the iteration.

Question1: Will this work? i.e. Is the fixed point of this procedure merely a local maximiser or global too? And does that depend on any properties of the matrix A?

Question2: Will the goal function zt A y increase in every iteration?