- #1
c0der
- 54
- 0
Hi,
With the following norm inequality:
||Av|| ≤ ||A||||v|| implies ||A|| = supv [ ||Av||/||v|| ]
I understand that sup is the upper bound of a set B, or least upper bound if B is a subset of A, where the upper bounds are elements of both B and A.
Is this saying that the norm of A is the maximum of the set ||Av||/||v||, where there are multiple vectors v being considered?
With the following norm inequality:
||Av|| ≤ ||A||||v|| implies ||A|| = supv [ ||Av||/||v|| ]
I understand that sup is the upper bound of a set B, or least upper bound if B is a subset of A, where the upper bounds are elements of both B and A.
Is this saying that the norm of A is the maximum of the set ||Av||/||v||, where there are multiple vectors v being considered?