Question

Unique best approximation in hilbert space intuition

Answer 1

Answer:

=> The notion of an orthonormal basis from linear algebra generalizes over to the case of Hilbert spaces. In a Hilbert space H, an orthonormal basis is a family {ek}k ∈ B of elements of H satisfying the conditions.

Thanks.. ;)

Answer 2

Explanation:

Best approximation This subsection employs the Hilbert projection theorem. If C is a non-empty closed convex subset of a Hilbert space H and x a point in H, there exists a unique point y ∈ C that minimizes the distance between x and points in C, ... More generally, this holds in any uniformly convex Banach space.