Editing Dimensional analysis (section)

=== Mechanics ===
The dimension of physical quantities of interest in [[mechanics]] can be expressed in terms of base dimensions T, L, and M – these form a 3-dimensional vector space. This is not the only valid choice of base dimensions, but it is the one most commonly used. For example, one might choose force, length and mass as the base dimensions (as some have done), with associated dimensions F, L, M; this corresponds to a different basis, and one may convert between these representations by a [[change of basis]]. The choice of the base set of dimensions is thus a convention, with the benefit of increased utility and familiarity. The choice of base dimensions is not entirely arbitrary, because they must form a [[Basis (linear algebra)|basis]]: they must [[Linear span|span]] the space, and be [[linearly independent]].

For example, F, L, M form a set of fundamental dimensions because they form a basis that is equivalent to T, L, M: the former can be expressed as [F = LM/T<sup>2</sup>], L, M, while the latter can be expressed as [T = (LM/F)<sup>1/2</sup>], L, M.

On the other hand, length, velocity and time (T, L, V) do not form a set of base dimensions for mechanics, for two reasons:
* There is no way to obtain mass – or anything derived from it, such as force – without introducing another base dimension (thus, they do not ''span the space'').
* Velocity, being expressible in terms of length and time ({{nowrap|1=V = L/T}}), is redundant (the set is not ''linearly independent'').