The set together with the energetic inner product is a pre-Hilbert space.
Equipped with this inner product, L is in fact complete.
This result is perhaps most transparent by considering the inner product defined above.
The relationship remains true independent of the frame in which the inner product is calculated.
The pairing between these two spaces also takes the form of an inner product.
This is slightly different than the above definition, which permits a change of inner product.
The inner product of two vectors is a complex number.
The inner product of the 4-acceleration and the 4-velocity is therefore always zero.
Two such vectors are adjacent when their inner product is 8.
We can calculate the value of n by considering the inner product.