The scalar product of a four-velocity and the corresponding four-acceleration is always 0.
This formula does not explicitly depend on the definition of the scalar product.
The prototypical example of a pseudoscalar is the scalar triple product.
The scalar product of the differential 4-position with itself is:
This scalar product of force and velocity is classified as instantaneous power.
The scalar products met in vector analysis are familiar examples of contraction.
(see above), the scalar product of d and m must be zero!
Another simple way to look at it as a scalar product of vectors in module 10.
The scalar triple product is invariant under rotation of the coordinate system.
This definition therefore depends on the definition of the scalar product.