Editing Galilean transformation (section)

==Translation==
[[Image:Standard conf.png|right|thumb|300px|Standard configuration of coordinate systems for Galilean transformations]]
Although the transformations are named for Galileo, it is the [[absolute time and space]] as conceived by [[Isaac Newton]] that provides their domain of definition. In essence, the Galilean transformations embody the intuitive notion of addition and subtraction of velocities as [[vector space|vectors]].

The notation below describes the relationship under the Galilean transformation between the coordinates {{math|(''x'', ''y'', ''z'', ''t'')}} and {{math|(''x''′, ''y''′, ''z''′, ''t''′)}} of a single arbitrary event, as measured in two coordinate systems {{math|S}} and {{math|S′}}, in uniform relative motion ([[velocity]] {{math|''v''}}) in their common {{math|''x''}} and {{math|''x''′}} directions, with their spatial origins coinciding at time {{math|1=''t'' = ''t''′ = 0}}:<ref>{{harvnb|Mould|2002|loc=[https://books.google.com/books?id=lfGE-wyJYIUC&pg=PA42 Chapter 2 §2.6, p. 42]}}</ref><ref>{{harvnb|Lerner|1996|loc=[https://books.google.com/books?id=B8K_ym9rS6UC&pg=PA1047 Chapter 38 §38.2, p. 1046,1047]}}</ref><ref>{{harvnb|Serway|Jewett|2006|loc=[https://books.google.com/books?id=1DZz341Pp50C&pg=PA261 Chapter 9 §9.1, p. 261]}}</ref><ref>{{harvnb|Hoffmann|1983|loc=[https://books.google.com/books?id=JokgnS1JtmMC&pg=PA83 Chapter 5, p. 83]}}</ref>

:<math>x' = x - v t </math>
:<math>y' = y </math>
:<math>z' = z </math>
:<math>t' = t .</math>

Note that the last equation holds for all Galilean transformations up to addition of a constant, and expresses the assumption of a universal time independent of the relative motion of different observers.

In the language of [[linear algebra]], this transformation is considered a [[shear mapping]], and is described with a matrix acting on a vector. With motion parallel to the ''x''-axis, the transformation acts on only two components:
:<math>\begin{pmatrix} x' \\t' \end{pmatrix} = \begin{pmatrix} 1 & -v \\0 & 1 \end{pmatrix}\begin{pmatrix} x \\t \end{pmatrix} </math>
Though matrix representations are not strictly necessary for Galilean transformation, they provide the means for direct comparison to transformation methods in special relativity.