In order to combine the three dimensions of length space and three dimensions of duration space in definitions for motion in six dimensions (3+3), it is necessary to use Jacobian matrices. The 3+1 and 1+3 dimensional definitions are simplifications of these.

Let matrices be written with upper case boldface. Let vectors be written in lowercase boldface and their magnitude without it.

Velocity = **V**, lenticity = **W**, displacement = **x**, distimement = **z**, independent distance = *s*, independent distime = *t*. The velocity **V** is defined by the matrix:

which is the Jacobian matrix of **x**(**t**) so that *V*_{ij} = ∂*x*_{i}/∂*z*_{j} for i, j = 1, 2, 3. If **z** is replaced with its independent magnitude, *t*, then **V** becomes **v**, which is

If **z** is replaced with its independent magnitude, *x*, then **V** → *v*, which is

The lenticity **W** is is defined by the matrix:

which is the Jacobian matrix of **t**(**s**) so that *W*_{ij} = ∂*z*_{i}/∂*x*_{j} for i, j = 1, 2, 3. If **x** is replaced by its independent magnitude, *s*, then **W** becomes **w**, which is

If **z** is replaced by its independent magnitude, *z*, then **W** → *w*, which is

Velocity may be weighted with mass *m* for momentum:

Lenticity may be weighted with vass *n* = 1/*m* for levamentum:

One may define other matrices similarly. Acceleration **A** is defined by the matrix:

which is the Jacobian matrix of **v**(**t**) so that *A*_{ij} = ∂*v*_{i}/∂*t*_{j} for i, j = 1, 2, 3. If **t** is reduced to its magnitude, *t*, then **A** becomes **a**, which is

Acceleration can be weighted with mass *m* for force:

Relentation **B** is defined by the matrix

which is the Jacobian matrix of **w**(**s**) so that *B*_{ij} = ∂*w*_{i}/∂*s*_{j} for i, j = 1, 2, 3. If **s** is reduced to its magnitude, *s*, then **B** becomes **b**, which is

Relentation can be weighted with vass *n* = 1/*m* for release: