Category:Definitions/Coordinate Transformations

This category contains definitions related to Coordinate Transformations.
Related results can be found in Category:Coordinate Transformations.

Let $\CC_\alpha$ and $\CC_\beta$ be coordinate systems over a space $\EE$ of $n$ dimensions.

Let $P$ be a point in $\EE$ such that:

$P$ is expressed as $\tuple {\alpha_1, \alpha_2, \ldots, \alpha_n}$ in $\CC_\alpha$

$P$ is expressed as $\tuple {\beta_1, \beta_2, \ldots, \beta_n}$ in $\CC_\beta$

A coordinate transformation is a mapping $\phi: \EE \to \EE$ such that:

$\map \phi {\alpha_1, \alpha_2, \ldots, \alpha_n} = \tuple {\beta_1, \beta_2, \ldots, \beta_n}$

for all such points in $\EE$.