Question

can someone help me read this wikipedia article, i cant understand it. it is about coordinate transformations

Answer 1

A coordinate transformation is a conversion from one system to another, to describe the same space. With every bijection from the space to itself two coordinate transformations can be associated: such that the new coordinates of the image of each point are the same as the old coordinates of the original point (the formulas for the mapping are the inverse of those for the coordinate transformation) such that the old coordinates of the image of each point are the same as the new coordinates of the original point (the formulas for the mapping are the same as those for the coordinate transformation)
For example, in 1D, if the mapping is a translation of 3 to the right, the first moves the origin from 0 to 3, so that the coordinate of each point becomes 3 less, while the second moves the origin from 0 to −3, so that the coordinate of each point becomes 3 more.

http://en.wikipedia.org/wiki/Coordinate_transformation#Transformations

Answer 2

what does wiki mean by the image of each point.

Answer 3

The value of the function at that point

Answer 4

ok so lets do a concrete exampe

Answer 5

i assume a bijection is an invertible function. Then suppose we have f : R^2 -> R^2
(x,y) -> (x+3, y+2). and the original plane has a circle with equation x^2 + y^2 = 1 .

Answer 6

so the bijection moves every point 3 right up 2

Answer 7

exactly