What conditions should vector x satisfy so that is bounded by a constant?
Suppose that is a vector with norm less than or equal to one . Let and define the following vector
How can I find a non-trivial subset of x that, regardless of the value of α, would result in where C is a constant that does not depend on n?
The above is satisfied when . For example, if then, we have . But I'm looking for a larger subset (or all x that satisfy the above conditions) than