The definition of the "dot product" of a general space varies quite a lot with different contexts.
Most definitions tend to be bilinear forms.
We use the unqualified generally refers to the dot product of Real coordinate spaces, which is a positive definite symmetric bilinear form. Other important examples include:
The rest of this section is about the case.
The default Euclidean space definition, we use the matrix representation of a symmetric bilinear form as the identity matrix, e.g. in :
- Bilinear form
- Bilinear map
- Bra-ket notation
- Complex dot product
- Definition of the indefinite orthogonal group
- Dirac Lagrangian
- Inner product
- Minkowski space
- Positive definite matrix
- Symmetric bilinear map
- The orthogonal group is the group of all matrices that preserve the dot product
- What happens to the definition of the orthogonal group if we choose other types of symmetric bilinear forms