In mathematics, a sequence of vectors (xn) in a Hilbert space
for all sequences of scalars (an) in the ℓp space ℓ2. A Riesz sequence is called a Riesz basis if
Theorems
If H is a finite-dimensional space, then every basis of H is a Riesz basis.
Let
and let
The first of the above conditions is the definition for (φn) to form a Riesz basis for the space it spans.